conditional intensity and gibbsianness of determinantal point processes the papangelou intensities of determinantal or fermion point processes are investigated these exhibit a monotonicity property expressing the repulsive nature of the interaction and satisfy a bound implying stochastic domination by a poisson point process we also show that determinantal point processes satisfy the so called condition which is a general form of gibbsianness under a continuity assumption the gibbsian conditional probabilities can be identified explicitly

average rate of downlink heterogeneous cellular networks over generalized fading channels a stochastic geometry approach in this paper we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks the framework leverages recent application of stochastic geometry to other cell interference modeling and analysis the heterogeneous cellular network is modeled as the superposition of many tiers of base stations bss having different transmit power density path loss exponent fading parameters and distribution and unequal biasing for flexible tier association a long term averaged maximum biased received power tier association is considered the positions of the bss in each tier are modeled as points of an independent poisson point process ppp under these assumptions we introduce a new analytical methodology to evaluate the average rate which avoids the computation of the coverage probability pcov and needs only the moment generating function mgf of the aggregate interference at the probe mobile terminal the distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions including composite fading channels with small and mid scale fluctuations in addition our method can efficiently handle correlated log normal shadowing with little increase of the computational complexity the proposed mgf based approach needs the computation of either a single or a two fold numerical integral thus reducing the complexity of pcov based frameworks which require for general fading distributions the computation of a four fold integral

holomorphic extensions of representations i automorphic functions let g be a connected real semisimple lie group contained in its complexification gc and let k be a maximal compact subgroup of g we construct a kc g double coset domain in gc and we show that the action of g on the k finite vectors of any irreducible unitary representation of g has a holomorphic extension to this domain for the resultant holomorphic extension of k finite matrix coefficients we obtain estimates of the singularities at the boundary as well as majorant minorant estimates along the boundary we obtain l bounds on holomorphically extended automorphic functions on g k in terms of sobolev norms and we use these to estimate the fourier coefficients of combinations of automorphic functions in a number of cases e g of triple products of maas forms

dirichlet form approach to infinite dimensional wiener processes with singular interactions we construct infinite dimensional wiener processes with interactions by constructing specific quasi regular dirichlet forms our assumptions are very mild accordingly our results can be applied to singular interactions such as hard core potentials lennard jones type potentials and dyson s model we construct nonequilibrium dynamics

power law shot noise the behavior of power law shot noise for which the associated impulse response functions assume a decaying power law form is explored expressions are obtained for the moments moment generating functions amplitude probability density functions autocorrelation functions and power spectral densities for a variety of parameters of the process for certain parameters the power spectral density exhibits 1 f type behavior over a substantial range of frequencies so that the process serves as a source of 1 f sup alpha shot noise for alpha in the range 0

correlation functions cluster functions and spacing distributions for random matrices the usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants from this representation one can deduce formulas for spacing probabilities in terms of fredholm determinants of matrix valued kernels the derivations of the various formulas are somewhat involved in this article we present a direct approach which leads immediately to scalar kernels for the unitary ensembles and matrix kernels for the orthogonal and symplectic ensembles and the representations of the correlation functions cluster functions and spacing distributions in terms of them

gaussian limit for determinantal random point fields author s soshnikov alexander abstract we prove that under fairly general conditions properly rescaled determinantal random point field converges to a generalized gaussian random process

downlink cellular network analysis with multi slope path loss models existing cellular network analyses and even simulations typically use the standard path loss model where received power decays like vert x vert alpha over a distance vert x vert this standard path loss model is quite idealized and in most scenarios the path loss exponent alpha is itself a function of vert x vert typically an increasing one enforcing a single path loss exponent can lead to orders of magnitude differences in average received and interference powers versus the true values in this paper we study multi slope path loss models where different distance ranges are subject to different path loss exponents we focus on the dual slope path loss function which is a piece wise power law and continuous and accurately approximates many practical scenarios we derive the distributions of sir snr and finally sinr before finding the potential throughput scaling which provides insight on the observed cell splitting rate gain the exact mathematical results show that the sir monotonically decreases with network density while the converse is true for snr and thus the network coverage probability in terms of sinr is maximized at some finite density with ultra densification network density goes to infinity there exists a phase transition in the near field path loss exponent alpha 0 if alpha 0 1 unbounded potential throughput can be achieved asymptotically if alpha 0 ultra densification leads in the extreme case to zero throughput

noncolliding brownian motion with drift and time dependent stieltjes wigert determinantal point process using the determinantal formula of biane bougerol and o connell we give multitime joint probability densities to the noncolliding brownian motion with drift where the number of particles is finite we study a special case such that the initial positions of particles are equidistant with a period a and the values of drift coefficients are well ordered with a scale we show that at each time t 0 the single time probability density of particle system is exactly transformed to the biorthogonal stieltjes wigert matrix model in the chern simons theory introduced by dolivet and tierz here one parameter extensions extensions of the stieltjes wigert polynomials which are themselves q extensions of the hermite polynomials play an essential role the two parameters a and of the process combined with time t are mapped to the parameters q and of the biorthogonal polynomials by the transformation of normalization factor of our probability density the partition function of the chern simons matrix model is readily obtained we study the determinantal structure of the matrix model and prove that at each time t 0 the present noncolliding brownian motion with drift is a determinantal point process in the sense that any correlation function is given by a determinant governed by a single integral kernel called the correlation kernel using the obtained correlation kernel we study time evolution of the noncolliding brownian motion with drift

cell edge aware precoding for downlink massive mimo cellular networks we propose a cell edge aware cea zero forcing zf precoder that exploits the excess spatial degrees of freedom provided by a large number of base station bs antennas to suppress inter cell interference at the most vulnerable user equipments ues we evaluate the downlink performance of cea zf as well as that of a conventional cell edge unaware ceu zf precoder in a network with a random bs topology our analysis and simulations show that the proposed cea zf precoder outperforms ceu zf precoding in terms of i aggregate per cell data rate ii coverage probability and iii 95 likely or edge user rate in particular when both perfect channel state information and a large number of antennas n are available at the bss we demonstrate that the outage probability under cea zf and ceu zf decay as 1 n 2 and 1 n respectively this result identifies cea zf as a more effective precoding scheme for massive multiple input multiple output mimo cellular networks our framework also reveals the importance of scheduling the optimal number of ues per bs and confirms the necessity to control the amount of pilot contamination received during the channel estimation phase

a generalization of permanents and determinants a method is developed for expanding arbitrary powers of the characteristic polynomial of a matrix the coefficients are expressed in terms of matrix functions generalizing those of the permanent and determinant the expansions have applications in probability theory

a variational principle in the dual pair of reproducing kernel hilbert spaces and an application given a positive definite bounded linear operator a on the hilbert space mathcal h 0 l2 e we consider a reproducing kernel hilbert space mathcal h with a reproducing kernel a x y here e is any countable set and a x y x y e is the representation of a w r t the usual basis of mathcal h 0 imposing further conditions on the operator a we also consider another reproducing kernel hilbert space mathcal h with a kernel function b x y which is the representation of the inverse of a in a sense so that mathcal h mathcal h 0 mathcal h becomes a rigged hilbert space we investigate the ratios of determinants of some partial matrices of a and b we also get a variational principle on the limit ratios of these values we apply this relation to show the gibbsianness of the determinantal point process or fermion point process defined by the operator a i a 1 on the set e

determinantal point processes associated with hilbert spaces of holomorphic functions we study determinantal point processes on mathbb c induced by the reproducing kernels of generalized fock spaces as well as those on the unit disc mathbb d induced by the reproducing kernels of generalized bergman spaces in the first case we show that all reduced palm measures of the same order are equivalent the radon nikodym derivatives are computed explicitly using regularized multiplicative functionals we also show that these determinantal point processes are rigid in the sense of ghosh and peres hence reduced palm measures of different orders are singular in the second case we show that all reduced palm measures of all orders are equivalent the radon nikodym derivatives are computed using regularized multiplicative functionals associated with certain blaschke products the quasi invariance of these determinantal point processes under the group of diffeomorphisms with compact supports follows as a corollary

analyzing the impact of access point density on the performance of finite area networks assuming a network of infinite extent several researchers have analyzed small cell networks using a poisson point process ppp location model leading to simple analytic expressions the general assumption has been that these results apply to finite area networks as well however do the results of infinite area networks apply to finite area networks in this paper we answer this question by obtaining an accurate approximation for the achievable signal to interference plus noise ratio sinr and user capacity in the downlink of a finite area network with a fixed number of access points aps the aps are uniformly distributed within the area of interest our analysis shows that crucially the results of infinite area networks are very different from those for finite area networks of low to medium ap density comprehensive simulations are used to illustrate the accuracy of our analysis for practical values of signal transmit powers and ap densities the analytic expressions capture the behavior of the system well as an added benefit the formulations developed here can be used in parametric studies for network design here the analysis is used to obtain the required number of aps to guarantee a desired target capacity in a finite area network

scale invariance of the png droplet and the airy process we establish that the static height fluctuations of a particular growth model the png droplet converges upon proper rescaling to a limit process which we call the airy process a y the airy process is stationary it has continuous sample paths its single time fixed y distribution is the tracy widom distribution of the largest eigenvalue of a gue random matrix and the airy process has a slow decay of correlations as y 2 roughly the airy process describes the last line of dyson s brownian motion model for random matrices our construction uses a multi layer version of the png model which can be analyzed through fermionic techniques specializing our result to a fixed value of y one reobtains the celebrated result of baik deift and johansson on the length of the longest increasing subsequence of a random permutation

on certain domains in cycle spaces of flag manifolds the affine homogeneous space g bbb c k bbb c associated to a real semi simple lie group g with maximal compact subgroup k contains a number of naturally defined it g invariant neighborhoods of its real points m bbb r g k which are of interest from various points of view here the universal iwasawa domain omega i is introduced from the point of view of incidence geometry and certain of its properties are derived e g it is stein kobayashi hyperbolic and contains the domain omega ag introduced by akhiezer and gindikin which is now known to be equivalent to the maximal domain of definition omega adp of the adapted complex structure associated to the killing metric in the tangent bundle tm bbb r one of the main goals of the paper is to develop methods which lead to a better understanding of the wolf domain omega w d of cycles in an open g orbit d in a flag manifold g bbb c p the key is the schubert domain omega s d which is defined by schubert cycles of complementary dimension to the cycles these are defined by a borel subgroup containing an iwasawa factor an and consequently omega s d and omega i are closely related

an example of a generalized brownian motion we present an example of a generalized brownian motion it is given by creation and annihilation operators on a twisted fock space ofl2 these operators fulfill for a fixed 1 1 the relationsc f c g c g c f f g 1 f g l2 we show that the distribution of these operators with respect to the vacuum expectation is a generalized gaussian distribution in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula we also indicate that our brownian motion is one component of ann dimensional brownian motion which is invariant under the quantum groups u n of woronowicz with v2

development of a fast method for determining psychophysical tuning curves a psychophysical tuning curve ptc is usually measured by determining the level of a narrowband noise required to mask a fixed low level tone for several masker center frequencies ptcs could be useful clinically for assessing frequency selectivity and for the diagnosis of dead regions in the cochlea when the signal frequency falls in a dead region the tip of the ptc is shifted away from the signal frequency however ptcs determined in the traditional way are too time consuming for use in clinical practice a fast method for determining ptcs is being developed and evaluated this uses a band of noise that sweeps in center frequency a bekesy method is used to track the masker level required for threshold for normally hearing subjects the new method gives stable results and ptcs similar in shape to those determined in the traditional way when the masker sweeps over a 2 octave range in about 4 minutes and the level changes by 1 2 db s preliminary results using hearing impaired subjects also show a good agreement with the traditional method however further work is required to determine optimum values for the noise bandwidth and rate of change of frequency and level

design modeling and performance analysis of multi antenna heterogeneous cellular networks this paper presents a stochastic geometry based framework for the design and analysis of downlink multi user multiple input multiple output mimo heterogeneous cellular networks with linear zero forcing transmit precoding and receive combining assuming rayleigh fading channels and perfect channel state information the generalized tiers of base stations may differ in terms of their poisson point process spatial density number of transmit antennas transmit power artificial biasing weight and number of user equipments served per resource block the spectral efficiency of a typical user equipped with multiple receive antennas is characterized using a non direct moment generating function based methodology with closed form expressions of the useful received signal and aggregate network interference statistics systematically derived in addition the area spectral efficiency is formulated under different space division multiple access and single user beamforming transmission schemes we examine the impact of different cellular network deployments propagation conditions antenna configurations and mimo setups on the achievable performance through theoretical and simulation studies based on the state of the art system parameters the results highlight the inherent limitations of baseline single input single output transmission and conventional sparse macro cell deployment as well as the promising potential of multi antenna communications and small cell solution in interference limited cellular environments

quantum α determinant cyclic modules of uq gln abstract as a particular one parameter deformation of the quantum determinant we introduce a quantum determinant det q and study the u q gl n cyclic module generated by it we show that the multiplicity of each irreducible representation in this cyclic module is determined by a certain polynomial called the q content discriminant a part of the present result is a quantum counterpart for the result of matsumoto and wakayama s matsumoto m wakayama alpha determinant cyclic modules of gl n c j lie theory 16 2006 393 405 however a new distinguished feature arises in our situation specifically we determine the degeneration of the multiplicities for classical singular points and give a general conjecture for singular points involving semi classical and quantum singularities moreover we introduce a quantum permanent per q and establish another conjecture which describes a reciprocity between the multiplicities of the irreducible summands of the cyclic modules generated respectively by det q and per q

transmission capacity of wireless ad hoc networks with outage constraints in this paper upper and lower bounds on the transmission capacity of spread spectrum ss wireless ad hoc networks are derived we define transmission capacity as the product of the maximum density of successful transmissions multiplied by their data rate given an outage constraint assuming that the nodes are randomly distributed in space according to a poisson point process we derive upper and lower bounds for frequency hopping fh cdma and direct sequence ds cdma ss networks which incorporate traditional modulation types no spreading as a special case these bounds cleanly summarize how ad hoc network capacity is affected by the outage probability spreading factor transmission power target signal to noise ratio snr and other system parameters using these bounds it can be shown that fh cdma obtains a higher transmission capacity than ds cdma on the order of m sup 1 2 spl alpha where m is the spreading factor and spl alpha 2 is the path loss exponent a tangential contribution is an apparently novel technique for obtaining tight bounds on tail probabilities of additive functionals of homogeneous poisson point processes

holomorphic extension of eigenfunctions let x g k be a riemannian symmetric space of non compact type we prove a theorem of holomorphic extension for eigenfunctions of the laplace beltrami operator on x by techniques from the theory of partial differential equations

success probability and area spectral efficiency in multiuser mimo hetnets we derive a general and closed form result for the success probability in downlink multiple antenna mimo heterogeneous cellular networks hetnets utilizing a novel toeplitz matrix representation this main result which is equivalently the signal to interference ratio sir distribution includes multiuser mimo single user mimo and per tier biasing for k different tiers of randomly placed base stations bss assuming zero forcing precoding and perfect channel state information the large sir limit of this result admits a simple closed form that is accurate at moderate sirs e g above 5 db these results reveal that the sir invariance property of siso hetnets does not hold for mimo hetnets instead the success probability may decrease as the network density increases we prove that the maximum success probability is achieved by activating only one tier of bss while the maximum area spectral efficiency ase is achieved by activating all the bss this reveals a unique tradeoff between the ase and link reliability in multiuser mimo hetnets to achieve the maximum ase while guaranteeing a certain link reliability we develop efficient algorithms to find the optimal bs densities it is shown that as the link reliability requirement increases more bss and more tiers should be deactivated

determinantal point processes and fermion quasifree states determinantal point processes are characterized by a special structural property of the correlation functions they are given by minors of a correlation kernel however unlike the correlation functions themselves this kernel is not defined intrinsically and the same determinantal process can be generated by many different kernels the non uniqueness of a correlation kernel causes difficulties in studying determinantal processes we propose a formalism which allows to find a distinguished correlation kernel under certain additional assumptions the idea is to exploit a connection between determinantal processes and quasifree states on car the algebra of canonical anticommutation relations we prove that the formalism applies to discrete n point orthogonal polynomial ensembles and to some of their large n limits including the discrete sine process and the determinantal processes with the discrete hermite laguerre and jacobi kernels investigated by borodin and olshanski commun math phys 353 853 903 2017 as an application we resolve the equivalence disjointness dichotomy for some of those processes

gaussian fluctuation for the number of particles in airy bessel sine and other determinantal random point fields we prove the central limit theorem clt for the number of eigenvalues near the spectrum edge for certain hermitian ensembles of random matrices to derive our results we use a general theorem essentially due to costin and lebowitz concerning the gaussian fluctuation of the number of particles in random point fields with determinantal correlation functions as another corollary of the costin lebowitz theorem we prove the clt for the empirical distribution function of the eigenvalues of random matrices from classical compact groups

a tractable framework for the analysis of dense heterogeneous cellular networks this paper investigates the downlink performance of dense k tier heterogeneous cellular networks hcns under general settings first gaussian approximation bounds for the standardized aggregate wireless interference awi in dense k tier hcns are obtained for when base stations bss in each tier are distributed over the plane according to a spatial and general poisson point process the kolmogorov smirnov ks distance is used to measure deviations of the distribution of the standardized awi from the standard normal distribution an explicit and analytical expression bounding the ks distance between these two distributions is obtained as a function of a broad range of network parameters such as per tier transmission power levels per tier bs intensity bs locations general fading statistics and general bounded path loss models bounds achieve a good statistical match between the standardized awi distribution and its normal approximation even for moderately dense hcns second various spatial performance metrics of interest such as outage capacity ergodic capacity and area spectral efficiency in the downlink of k tier hcns for general signal propagation models are investigated by making use of the derived distribution approximation results considering two specific bs association policies it is shown that the derived performance bounds track the actual performance metrics reasonably well for a wide range of bs intensities with the gap among them becoming negligibly small for denser hcn deployments finally both analytical and numerical results on the area spectral efficiency reveal a non linear growth trend with diminishing returns of hcn performance hence the sf sir invariance property does not hold under bounded path loss models which is a critical finding from the hcn design perspective in particular it points out a critical bs density beyond which the hcn performance starts to decline due to excessive wireless interference

gaussian and non gaussian random fields associated with markov processes to every markov process with a symmetric transition density there correspond two random fields over the state space a gaussian field the free field and the occupation field t which describes amount of time the particle spends at each state a relation between these two random fields is established which is useful both for the field theory and theory of markov processes

sampling bias and logistic models summary in a regression model the joint distribution for each finite sample of units is determined by a function px y depending only on the list of covariate values x x u1 x un on the sampled units no random sampling of units is involved in biological work random sampling is frequently unavoidable in which case the joint distribution p y x depends on the sampling scheme regression models can be used for the study of dependence provided that the conditional distribution p y x for random samples agrees with px y as determined by the regression model for a fixed sample having a non random configuration x the paper develops a model that avoids the concept of a fixed population of units thereby forcing the sampling plan to be incorporated into the sampling distribution for a quota sample having a predetermined covariate configuration x the sampling distribution agrees with the standard logistic regression model with correlated components for most natural sampling plans such as sequential or simple random sampling the conditional distribution p y x is not the same as the regression distribution unless px y has independent components in this sense most natural sampling schemes involving binary random effects models are biased the implications of this formulation for subject specific and population averaged procedures are explored

system of complex brownian motions associated with the o connell process the o connell process is a softened version a geometric lifting with a parameter a 0 of the noncolliding brownian motion such that neighboring particles can change the order of positions in one dimension within the characteristic length a this process is not determinantal under a special entrance law however borodin and corwin gave a fredholm determinant expression for the expectation of an observable which is a softening of an indicator of a particle position we rewrite their integral kernel to a form similar to the correlation kernels of determinantal processes and show if the number of particles is n the rank of the matrix of the fredholm determinant is n then we give a representation for the quantity by using an n particle system of complex brownian motions cbms the complex function which gives the determinantal expression to the weight of cbm paths is not entire but in the combinatorial limit a 0 it becomes an entire function providing conformal martingales and the cbm representation for the noncolliding brownian motion is recovered

on the correlation measure of a family of commuting hermitian operators with applications to particle densities of the quasi free representations of the car and ccr let x be a locally compact second countable hausdorff topological space we consider a family of commuting hermitian operators a indexed by all measurable relatively compact sets in x a quantum stochastic process over x for such a family we introduce the notion of a correlation measure we prove that if the family of operators possesses a correlation measure which satisfies some condition of growth then there exists a point process over x having the same correlation measure furthermore the operators a can be realized as multiplication operators in the l2 space with respect to this point process in the proof we utilize the notion of positive definiteness proposed in y g kondratiev t kuna harmonic analysis on the configuration space i general theory infin dimens anal quantum probab relat top 5 2002 201 233 in particular our result extends the criterion of existence of a point process from that paper to the case of the topological space x which is a standard underlying space in the theory of point processes as applications we discuss particle densities of the quasi free representations of the car and ccr which lead to fermion boson fermion like and boson like e g para fermions and para bosons of order 2 point processes in particular we prove that any fermion point process corresponding to a hermitian kernel may be derived in this way

statistical modeling and probabilistic analysis of cellular networks with determinantal point processes although the poisson point process ppp has been widely used to model base station bs locations in cellular networks it is an idealized model that neglects the spatial correlation among bss this paper proposes the use of the determinantal point process dpp to take into account these correlations in particular the repulsiveness among macro bs locations dpps are demonstrated to be analytically tractable by leveraging several unique computational properties specifically we show that the empty space function the nearest neighbor function the mean interference and the signal to interference ratio sir distribution have explicit analytical representations and can be numerically evaluated for cellular networks with dpp configured bss in addition the modeling accuracy of dpps is investigated by fitting three dpp models to real bs location data sets from two major u s cities using hypothesis testing for various performance metrics of interest we show that these fitted dpps are significantly more accurate than popular choices such as the ppp and the perturbed hexagonal grid model

exact sinr statistics in the presence of heterogeneous interferers we derive new results for the higher order moments of signal to interference plus noise ratio sinr in the presence of an arbitrary poisson point process ppp based heterogeneous interference field the analysis leverages on a moment generating function mgf methodology which only requires the statistics of intended signal and aggregate interference thus eliminating the need for the exact distribution of sinr we extend the existing results on interference statistics by deriving a generalized closed form expression of the interference mgf considering nakagami m fading channels with exclusion region in certain special cases explicit expressions for the averages of different functions of sinr are found which also lead to closed form solutions for the probability distributions of aggregate interference reciprocal and signal to interference ratio we prove that in such cases the effect of total ppp based interference power on useful transmission is mathematically equivalent to the severe fluctuations from a one sided gaussian fading channel as an application example the proposed methodology is used together with stochastic geometry theory to characterize the average sinr and rate in heterogeneous cellular networks the validity of our analytical derivations is confirmed via monte carlo simulations for various system settings we show that with cellular network densification there exists a tradeoff between the average sinr and rate performance

gibbsianness of fermion random point fields we consider fermion or determinantal random point fields on euclidean space d given a bounded translation invariant and positive definite integral operator j on l2 d we introduce a determinantal interaction for a system of particles moving on d as follows the n points located at x1 x n d have the potential energy given by where j x y is the integral kernel function of the operator j we show that the gibbsian specification for this interaction is well defined when j is of finite range in addition and for d 2 if the intensity is small enough we show that the fermion random point field corresponding to the operator j i j 1 is a gibbs measure admitted to the specification

series expansion for interference in wireless networks the spatial correlations in transmitter node locations introduced by common multiple access protocols make the analysis of interference outage and other related metrics in a wireless network extremely difficult most works therefore assume that nodes are distributed either as a poisson point process ppp or a grid and utilize the independence properties of the ppp or the regular structure of the grid to analyze interference outage and other metrics but the independence of node locations makes the ppp a dubious model for nontrivial macs which intentionally introduce correlations e g spatial separation while the grid is too idealized to model real networks in this paper we introduce a new technique based on the factorial moment expansion of functionals of point processes to analyze functions of interference in particular outage probability we provide a taylor series type expansion of functions of interference wherein increasing the number of terms in the series provides a better approximation at the cost of increased complexity of computation various examples illustrate how this new approach can be used to find outage probability in both poisson and non poisson wireless networks

construction of point processes for classical and quantum gases we propose a construction of point processes via the method of cluster expansion the important role of the class of infinitely divisible point processes is noted examples are permanental and determinantal processes as well as the classical gibbs point processes where the interaction is given by a stable and regular pair potential

modeling heterogeneous network interference using poisson point processes cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells relays and distributed antennas unfortunately the resulting interference environment is also becoming more complicated making evaluation of different communication strategies challenging in both analysis and simulation leveraging recent applications of stochastic geometry to analyze cellular systems this paper proposes to analyze downlink performance in a fixed size cell which is inscribed within a weighted voronoi cell in a poisson field of interferers a nearest out of cell interferer out of cell interferers outside a guard region and cross tier interferers are included in the interference calculations bounding the interference power as a function of distance from the cell center the total interference is characterized through its laplace transform an equivalent marked process is proposed for the out of cell interference under additional assumptions to facilitate simplified calculations the interference distribution is approximated using the gamma distribution with second order moment matching the gamma approximation simplifies calculation of the success probability and average rate incorporates small scale and large scale fading and works with co tier and cross tier interference simulations show that the proposed model provides a flexible way to characterize outage probability and rate as a function of the distance to the cell edge

absolute continuity and singularity of palm measures of the ginibre point process we prove a dichotomy between absolute continuity and singularity of the ginibre point process mathsf g and its reduced palm measures mathsf g mathbf x mathbf x in mathbb c ell ell 0 1 2 ldots namely reduced palm measures mathsf g mathbf x and mathsf g mathbf y for mathbf x in mathbb c ell and mathbf y in mathbb c n are mutually absolutely continuous if and only if ell n they are singular each other if and only if ell not n furthermore we give an explicit expression of the radon nikodym density d mathsf g mathbf x d mathsf g mathbf y for mathbf x mathbf y in mathbb c ell

effects of low pass filtering on the intelligibility of speech in noise for people with and without dead regions at high frequencies people with high frequency sensorineural hearing loss differ in the benefit they gain from amplification of high frequencies when listening to speech using vowel consonant vowel vcv stimuli in quiet that were amplified and then low pass filtered with various cutoff frequencies vickers et al j acoust soc am 110 1164 1175 2001 found that the benefit from amplification of high frequency components was related to the presence or absence of a cochlear dead region at high frequencies for hearing impaired subjects without dead regions performance improved with increasing cutoff frequency up to 7 5 khz the highest value tested subjects with high frequency dead regions showed no improvement when the cutoff frequency was increased above about 1 7 times the edge frequency of the dead region the present study was similar to that of vickers et al but used vcv stimuli presented in background noise ten subjects with high frequency hearing loss including eight from the study of vickers et al were tested five had dead regions starting below 2 khz and five had no dead regions speech stimuli at a nominal level of 65 db were mixed with spectrally matched noise amplified according to the cambridge prescriptive formula for each subject and then low pass filtered the noise level was chosen separately for each subject to give a moderate reduction in intelligibility relative to listening in quiet for subjects without dead regions performance generally improved with increasing cutoff frequency up to 7 5 khz on average more so in noise than in quiet for most subjects with dead regions performance improved with cutoff frequency up to 1 5 2 times the edge frequency of the dead region but hardly changed with further increases calculations of speech audibility using a modified version of the articulation index showed that application of the cambridge formula was at least partially successful in making high frequency components of the speech audible for subjects with dead regions and that such subjects often failed to benefit from increased audibility of the speech at high frequencies

large deviations for the fermion point process associated with the exponential kernel for the fermion point process on the whole complex plane associated with the exponential kernel e z bar w we show the central limit theorem for the random variable d r the number of points inside the ball d r of radius r as r and we establish the large deviation principle for the random variables r 2 d r r 0

a mathematical framework to the computation of the error probability of downlink mimo cellular networks by using stochastic geometry in this paper a mathematical framework to the computation of the error probability of downlink cellular networks is introduced it is based on the poisson point process ppp based abstraction for modeling the spatial locations of the base stations bss and it exploits results from stochastic geometry for characterizing the distribution of the other cell interference the framework is applicable to spatial multiplexing multiple input multiple output mimo systems with an arbitrary number of antennas at the transmitter n t and at the receiver n r if n t n r 1 the mathematical approach can be used for arbitrary fading distributions on both useful and interfering links if either n t 1 or n r 1 it can be applied to arbitrary fading distributions on the useful link and to rayleigh fading on the interfering links it is shown that the proposed approach leads to easy to compute integral expressions which reduce to closed form formulas in some asymptotic regimes furthermore the framework is shown to provide insights for system design and optimization the accuracy of the mathematical analysis is substantiated through extensive monte carlo simulations for various cellular network setups

j hermitian determinantal point processes balanced rigidity and balanced palm equivalence we study palm measures of determinantal point processes with j hermitian correlation kernels a point process mathbb p on the punctured real line mathbb r mathbb r sqcup mathbb r is said to be balanced rigid if for any precompact subset b subset mathbb r the difference between the numbers of particles of a configuration inside b cap mathbb r and b cap mathbb r is almost surely determined by the configuration outside b the point process mathbb p is said to have the balanced palm equivalence property if any reduced palm measure conditioned at 2n distinct points n in mathbb r and n in mathbb r is equivalent to mathbb p we formulate general criteria for determinantal point processes with j hermitian correlation kernels to be balanced rigid and to have the balanced palm equivalence property and prove in particular that the determinantal point processes with whit taker kernels of borodin and olshanski are balanced rigid and have the balanced palm equivalence property

the central limit theorem for local linear statistics in classical compact groups and related combinatorial identities author s soshnikov alexander abstract we discuss clt for the global and local linear statistics of random matrices from classical compact groups the main part of our proofs are certain combinatorial identities much in the spirit of works by kac and spohn

harmonic analysis on the infinite dimensional unitary group and determinantal point processes the infinite dimensional unitary group u is the inductive limit of growing compact unitary groups u n in this paper we solve a problem of harmonic analysis on u stated in ol3 the problem consists in computing spectral decomposition for a remarkable 4 parameter family of characters of u these characters generate representations which should be viewed as analogs of nonexisting regular representation of u the spectral decomposition of a character of u is described by the spectral measure which lives on an infinite dimensional space of indecomposable characters the key idea which allows us to solve the problem is to embed into the space of point configurations on the real line without two points this turns the spectral measure into a stochastic point process on the real line the main result of the paper is a complete description of the processes corresponding to our concrete family of characters we prove that each of the processes is a determinantal point process that is its correlation functions have determinantal form with a certain kernel our kernels have a special integrable form and are expressed through the gauss hypergeometric function from the analytic point of view the problem of computing the correlation kernels can be reduced to a problem of evaluating uniform asymptotics of certain discrete orthogonal polynomials studied earlier by richard askey and peter lesky one difficulty lies in the fact that we need to compute the asymptotics in the oscillatory regime with the period of oscillations tending to 0 we do this by expressing the polynomials in terms of a solution of a discrete riemann hilbert problem and computing the nonoscillatory asymptotics of this solution from the point of view of statistical physics we study thermodynamic limit of a discrete log gas system an interesting feature of this log gas is that its density function is asymptotically equal to the characteristic function of an interval our point processes describe how different the random particle configuration is from the typical densely packed configuration in simpler situations of harmonic analysis on infinite symmetric groups and harmonic analysis of unitarily invariant measures on infinite hermitian matrices similar results were obtained in our papers bo1 bo2 bo4

oscillatory matrix model in chern simons theory and jacobi theta determinantal point process the partition function of the chern simons theory on the three sphere with the unitary group u n provides a one matrix model the corresponding n particle system can be mapped to the determinantal point process whose correlation kernel is expressed by using the stieltjes wigert orthogonal polynomials the matrix model and the point process are regarded as q extensions of the random matrix model in the gaussian unitary ensemble and its eigenvalue point process respectively we prove the convergence of the n particle system to an infinite dimensional determinantal point process in n in which the correlation kernel is expressed by jacobi s theta functions we show that the matrix model obtained by this limit realizes the oscillatory matrix model in chern simons theory discussed by de haro and tierz

local central limit theorem for determinantal point processes we prove a local central limit theorem lclt for the number of points n j in a region j in mathbb r d specified by a determinantal point process with an hermitian kernel the only assumption is that the variance of n j tends to infinity as j rightarrow infty this extends a previous result giving a weaker central limit theorem for these systems our result relies on the fact that the lee yang zeros of the generating function for e k j the probabilities of there being exactly k points in j all lie on the negative real z axis in particular the result applies to the scaled bulk eigenvalue distribution for the gaussian unitary ensemble gue and that of the ginibre ensemble for the gue we can also treat the properly scaled edge eigenvalue distribution using identities between gap probabilities the lclt can be extended to bulk eigenvalues of the gaussian symplectic ensemble a lclt is also established for the probability density function of the k th largest eigenvalue at the soft edge and of the spacing between k th neighbors in the bulk

α pfaffian pfaffian point process and shifted schur measure abstract for any complex number and any even size skew symmetric matrix b we define a generalization pf b of the pfaffian pf b which we call the pfaffian the pfaffian is a pfaffian analogue of the determinant studied in t shirai and y takahashi j funct anal 205 2003 414 463 and d vere jones linear algebra appl 111 1988 119 124 it gives the pfaffian at 1 we give some formulas for pfaffians and study the positivity further we define point processes determined by the pfaffian also we provide a linear algebraic proof of the explicit pfaffian expression obtained in s matsumoto correlation functions of the shifted schur measure math co 0312373 for the correlation function of the shifted schur measure

approximating the α permanent summary the standard matrix permanent is the solution to a number of combinatorial and graph theoretic problems and the weighted permanent is the density function for a class of cox processes called boson processes the exact computation of the ordinary permanent is known to be p complete and the same appears to be the case for the permanent for most values of at present the lack of a satisfactory algorithm for approximating the permanent is a formidable obstacle to the use of boson processes in applied work this paper proposes an importance sampling estimator using nonuniform random permutations generated in a cycle format empirical investigation reveals that the estimator works well for the sorts of matrices that arise in point process applications involving up to a few hundred points we conclude with a numerical illustration of the bayes estimate of the intensity function of a boson point process which is a ratio of permanents

the complex crown for homogeneous harmonic spaces the complex crown of a noncompact riemannian symmetric space x g k is generalized to the case of homogeneous harmonic spaces s na we prove that every eigenfunction of the laplace beltrami operator on s extends holomorphically to the crown and that the crown is the maximal s invariant domain in sc with this property

on optimal downlink coverage in poisson cellular networks with power density constraints this paper studies downlink coverage maximization for cellular networks in which base station bs locations are modeled using a spatial poisson point process considering three different coverage models and under constraints on transmit power bs density and transmit power density firstly the coverage optimization problem is solved analytically for the first coverage model that focuses on noise limited communication by ignoring interference and random fading effects this model provides useful insights into the significance of bounded path loss models to obtain meaningful solutions for this problem the other two coverage models are based on the users received signal to interference plus noise ratio sinr from their associated bss for these models it is shown that the coverage optimization problem can be reduced to a constrained single dimensional optimization problem without any loss of optimality the related solutions can be obtained with limited computational complexity by resorting to a numerical search over a compact subset of candidate values bounds on the optimum bs density are also provided to further truncate the search space all results are derived for general bounded path loss models specific applications are also illustrated to provide further design insights and to highlight the importance of using bounded path loss models for coverage analysis

markov loops and renormalization we study the poissonnian ensembles of markov loops and the associated renormalized self intersection local times

noncolliding brownian motion and determinantal processes a system of one dimensional brownian motions bms conditioned never to collide with each other is realized as i dyson s bm model which is a process of eigenvalues of hermitian matrix valued diffusion process in the gaussian unitary ensemble gue and as ii the h transform of absorbing bm in a weyl chamber where the harmonic function h is the product of differences of variables the vandermonde determinant the karlin mcgregor formula gives determinantal expression to the transition probability density of absorbing bm we show from the karlin mcgregor formula if the initial state is in the eigenvalue distribution of gue the noncolliding bm is a determinantal process in the sense that any multitime correlation function is given by a determinant specified by a matrix kernel by taking appropriate scaling limits spatially homogeneous and inhomogeneous infinite determinantal processes are derived we note that the determinantal processes related with noncolliding particle systems have a feature in common such that the matrix kernels are expressed using spectral projections of appropriate effective hamiltonians on the common structure of matrix kernels continuity of processes in time is proved and general property of the determinantal processes is discussed

zeros of the i i d gaussian power series a conformally invariant determinantal process consider the zero set of the random power series f z p anz n with i i d complex gaussian coefficientsan we show that these zeros form a determinantal process more precisely their joint intensity can be written as a minor of the bergman kernel we show that the number of zeros of f in a disk of radius r about the origin has the same distribution as the sum of independent 0 1 valued random variables xk where p xk 1 r 2k moreover the set of absolute values of the zeros of f has the

quasi invariance and integration by parts for determinantal and permanental processes abstract determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent their atoms exhibit mutual attraction of repulsion thus these processes are very far from the uncorrelated situation encountered in poisson models we establish a quasi invariance result we show that if atom locations are perturbed along a vector field the resulting process is still a determinantal respectively permanental process the law of which is absolutely continuous with respect to the original distribution based on this formula following bismut approach of malliavin calculus we then give an integration by parts formula

comparisons of frequency selectivity in simultaneous and forward masking for subjects with unilateral cochlear impairments two experiments are described in which frequency selectivity was estimated in simultaneous and forward masking for each ear of subjects with moderate 25 60 db hl unilateral cochlear hearing losses in both experiments the signal level was fixed for a given ear and type of masking simultaneous or forward and the masker level was varied to determine threshold using an adaptive two alternative forced choice procedure in experiment i the masker was a noise with a spectral notch centered at the signal frequency either 1 0 or 1 5 khz threshold was determined as a function of notch width signal levels were chosen so that the noise level required at threshold for a notch width of zero was similar for the normal and impaired ear of each subject in both simultaneous and forward masking the function relating threshold to notch width had a steeper slope for the normal ear than for the impaired ear of each subject for the normal ears these functions were steeper in forward masking than in simultaneous masking this difference was interpreted as resulting from suppression for the impaired ears significant differences in the same direction were observed for three of the five subjects but the differences were smaller in experiment ii psychophysical tuning curves ptcs were determined in the presence of a fixed notched noise centered at the signal frequency 1 0 khz for the normal ears the ptcs were sharper in forward masking than in simultaneous masking for the impaired ears the ptcs were similar in simultaneous and forward masking but those in forward masking tended to be sharper at masker frequencies far removed from the signal frequency overall the results suggest that suppression is reduced but not completely absent in cases of moderate cochlear hearing loss

a random point field related to bose einstein condensation abstract the random point fields which describe the position distributions of the systems of ideal boson gas in states of bose einstein condensations are obtained through the thermodynamic limits the resulting point fields are given by convolutions of two kinds of independent point fields the so called boson processes whose generating functionals are represented by the inverses of the fredholm determinants for operators related to the heat operator and the point fields whose generating functionals are represented by the resolvents of the operators the construction of the latter point fields in an abstract formulation is also given

studying the sinr process of the typical user in poisson networks using its factorial moment measures based on a stationary poisson point process a wireless network model with random propagation effects shadowing and or fading is considered in order to examine the process formed by the signal to interference plus noise ratio sinr values experienced by a typical user with respect to all the base stations in the down link channel this sinr process is completely characterized by deriving its factorial moment measures which involve numerically tractable explicit integral expressions this novel framework naturally leads to expressions for the k coverage probability including the case of random sinr threshold values considered in multi tier network models while the k coverage probabilities correspond to the marginal distributions of the order statistics of the sinr process a more general relation is presented connecting the factorial moment measures of the sinr process to the joint densities of these order statistics this gives a way for calculating the exact values of the coverage probabilities arising in a general scenario of signal combination and interference cancellation between base stations the presented framework consisting of the mathematical representations of sinr characteristics with respect to the factorial moment measures holds for the whole domain of sinr and is amenable to considerable model extension

random point fields associated with certain fredholm determinants i fermion poisson and boson point processes we introduce certain classes of random point fields including fermion and boson point processes which are associated with fredholm determinants of certain integral operators and study some of their basic properties limit theorems correlation functions palm measures etc also we propose a conjecture on an analogue of the determinant and permanent

alpha determinant cyclic modules and jacobi polynomials for positive integers n and l we study the cyclic u gl n module generated by the l th power of the determinant det x this cyclic module is isomorphic to the n th tensor space s l n n of the symmetric l th tensor space of n for all but finitely many exceptional values of if is exceptional then the cyclic module is equivalent to a proper submodule of s l n n i e the multiplicities of several irreducible subrepresentations in the cyclic module are smaller than those in s l n n the degeneration of each isotypic component of the cyclic module is described by a matrix whose size is given by a kostka number and whose entries are polynomials in with rational coefficients in particular we determine the matrix completely when n 2 in this case the matrix becomes a scalar and is essentially given by a classical jacobi polynomial moreover we prove that these polynomials are unitary in the appendix we consider a variation of the spherical fourier transformation for o nl o n l as a main tool for analyzing the same problems and describe the case where n 2 by using the zonal spherical functions of the gelfand pair o 2l o 2 l

random point fields associated with certain fredholm determinants ii fermion shifts and their ergodic and gibbs properties we construct and study a family of probability measures on the configuration space over countable discrete space associated with nonnegative definite symmetric operators via determinants under a mild condition they turn out unique gibbs measures also some ergodic properties including the entropy positivity are discussed in the lattice case

asymptotics of plancherel measures for symmetric groups 1 1 plancherel measures given a finite group g by the corresponding plancherel measure we mean the probability measure on the set g of irreducible representations of g which assigns to a representation g the weight dim g for the symmetric group s n the set s n is the set of partitions of the number n which we shall identify with young diagrams with n squares throughout this paper the plancherel measure on partitions arises naturally in representation theoretic combinatorial and probabilistic problems for example the plancherel distribution of the first part of a partition coincides with the distribution of the longest increasing subsequence of a uniformly distributed random permutation 31 we denote the plancherel measure on partitions of n by mn