three transmit antenna space time codes based on su 3 fully diverse constellations i e a set of unitary matrices whose pairwise differences are nonsingular are useful in multiantenna communications especially in multiantenna differential modulation since they have good pairwise error properties recently group theoretic ideas especially fixed point free fpf groups have been used to design fully diverse constellations of unitary matrices here we give systematic design methods of space time codes which are appropriate for three transmit antenna differential modulation the structures of the codes are motivated by the special unitary lie group su 3 one of the codes which is called the ab code has a fast maximum likelihood ml decoding algorithm using complex sphere decoding diversity products of the codes can be easily calculated and simulated performance shows that they are better than group based codes especially at high rates and as good as the elaborately designed nongroup code

unitary space time constellations based on quasi orthogonal sequences in this paper we propose a novel class of unitary space time constellations based on quaternary quasi orthogonal sequences qoss minimizing the maximum correlation between the signal matrices the proposed design owing to the underlying algebraic structure of the qoss allows for an efficient decoder structure while offering performance virtually identical to the unitary space time constellation design by hochwald et al

exact large deviation bounds up to t c for the ising model in two dimensions we prove an upper large deviation bound for the block spin magnetization in the 2d ising model in the phase coexistence region the precise rate given by the wulff construction is shown to hold true for all c combined with the lower bounds derived in i those results yield an exact second order large deviation theory up to the critical temperature

multivariate spatial central limit theorems with applications to percolation and spatial graphs suppose x x x x in z d is a family of i i d variables in some measurable space b 0 is a bounded set in r d and for t 1 h t is a measure on t b 0 determined by the restriction of x to lattice sites in or adjacent to t b 0 we prove convergence to a white noise process for the random measure on b 0 given by t d 2 h t ta eh t ta for subsets a of b 0 as t becomes large subject to h satisfying a stabilization condition whereby the effect of changing x at a single site x is local but with no assumptions on the rate of decay of correlations we also give a multivariate central limit theorem for the joint distributions of two or more such measures h t and adapt the result to measures based on poisson and binomial point processes applications given include a white noise limit for the measure which counts clusters of critical percolation a functional central limit theorem for the empirical process of the edge lengths of the minimal spanning tree on random points and central limit theorems for the on line nearest neighbor graph

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

nd convolutional codes i performance analysis a noncoherent coded system which incorporates convolutional codes in conjunction of multiple symbol noncoherent detection is presented in this two part paper where part i focuses on the performance analysis of the system and part ii deals with the structural properties of the underlying convolutional codes these convolutional codes are referred to as nd convolutional codes it is shown that nd convolutional codes provide a general framework for various noncoherent coding systems including differential systems two models of the carrier phase are examined and the relationships between them is established for the first one the carrier phase remains constant for l channels signals whereas for the second one it unvaries throughout the transmission period the regular structure of nd codes facilitates the evaluation of a simple upper bound on the pairwise and bit error probabilities as well as a simple expression for the generalized cutoff rate the exponential rate of the error probability which is the single parameter governing the error performance at large signal to noise ratios is identified via large deviations techniques this parameter leads to the interesting conclusion that increasing l does not necessarily monotonically improve the error performance of the noncoherent system the same conclusion is reached by examining upper bounds and computer simulation results of several interesting examples these examples also reveal that optimal codes for coherent detection are not necessarily optimal for noncoherent detection and a search for good codes some of which are tabulated in part ii of the paper is required

hz algebra spectra are differential graded algebras we show that the homotopy theory of differential graded algebras coincides with the homotopy theory of h algebra spectra namely we construct quillen equivalences between the quillen model categories of unbounded differential graded algebras and h algebra spectra we also construct quillen equivalences between the differential graded modules and module spectra over these algebras we use these equivalences in turn to produce algebraic models for rational stable model categories we show that basically any rational stable model category is quillen equivalent to modules over a differential graded algebra with many objects

a central limit theorem for critical first passage percolation in two dimensions consider independent first passage percolation on the edges of 2 denote the passage time of the edge e in 2 by t e and assume that p t e 0 1 2 p 0 t e c 0 0 for some constant c 0 0 and that e t e 4 denote by b 0 n the passage time from 0 to the halfplane x y x n and by t 0 nu the passage time from 0 to the nearest lattice point to nu for u a unit vector we prove that there exist constants 0 c 1 c 2 and n such that c 1 log n 1 2 n c 2 log n 1 2 and such that n 1 b 0 n eb 0 n and 2 n 1 t 0 nu et 0 nu converge in distribution to a standard normal variable as n u fixed a similar result holds for the site version of first passage percolation on 2 when the common distribution of the passage times t v of the vertices satisfies p t v 0 1 p t v c 0 p c 2 site critical probability of site percolation on 2 and e t u 4

coverage problems for random intervals let t j j in mathbb z be the points of an inhomogeneous poisson process on mathbb r in any order let zeta j eta j j in mathbb z be a sequence of independent pairs of arbitrary nonnegative random variables that is independent of t j j in mathbb z in this paper properties of the random set s cup j varepsilon mathbb z t j xi j t j eta j are studied the main results are formulae for the probability that t x subset s where infty t leqq x infty i e t x is covered by s and for the distribution function of the length of the component of s with left endpoint t given that t is such a left endpoint the results have applications to infinite server queues with varying arrival rate

clump counts in a mosaic on decrit des proprietes de second ordre en utilisant la theorie limite et des methodes approchees

capacite et inegalite de faber krahn dans rn abstract in this paper we define a new capacity which allows us to control the behaviour of the dirichlet spectrum of a compact riemannian manifold with boundary with small subsets which may intersect the boundary removed this result generalises a classical result of rauch and taylor the crushed ice theorem in the second part we show that the dirichlet spectrum of a sequence of bounded euclidean domains converges to the spectrum of a ball with the same volume if the first eigenvalue of these domains converges to the first eigenvalue of a ball

trace orthonormal full diversity cyclotomic space time codes in this paper we consider the design of full diversity space time codes for a coherent multiple input multiple output mimo communication system starting from both the information theoretic and detection error viewpoints we first establish that a desirable property for general linear dispersion ld codes is to have an interunitary as well as an intraunitary structure a structure we call trace orthonormality by imposing the trace orthonormal structure on an ld code and applying cyclotomic number theory we establish for an arbitrary number of transmitter and receiver antennas a systematic and simple method to jointly design a unitary cyclotomic matrix the diophantine number and the corresponding constellation for an ld code as a result this enables us to construct full diversity rectangular cyclotomic ld codes with any symbol transmission rate less than or equal to the number of transmitter antennas in addition for the case when the number of transmitter antennas is greater than the number of receiver antennas by taking advantage of the delay we also arrive at the design of a special trace orthonormal full diversity cyclotomic space time block code which for the number of transmitter antenna being equal to 2m can be proved to minimize the worst case pairwise error probability of a maximum likelihood ml detector for a q ary quadrature amplitude modulation qam signal constellation and therefore achieves optimal coding gain computer simulations show that these codes have bit error performance advantages over currently available codes

stratified structure of the universe and burgers equation a probabilistic approach the model of the potential turbulence described by the 3 dimensional burgers equation with random initial data was developped by zeldovich and shandarin in order to explain the existing large scale structure of the universe most of the recent probabilistic investigations of large time asymptotics of the solution deal with the central limit type results the gaussian scenario under suitable moment assumptions on the initial velocity field these results and some open questions are discussed in sect 2 where we concentrate on the gaussian model and the shot noise model in sect 3 we construct a probabilistic model of strong initial fluctuations a zero range shot noise field with high amplitudes which reveals an intermittent large time behaviour with the velocity vec v t x determined by the position of the largest initial fluctuation discounted by the heat kernelg t x in a neighborhood ofx the asymptoties of such local maximum ast can be analyzed with the help of the theory of records sect 4 finally in sect 5 we introduce a global definition of a point process oft local maxima and show the weak convergence of the suitably rescaled process to a non trivial limit ast

faber krahn inequalities in sharp quantitative form the classical faber krahn inequality asserts that balls uniquely minimize the first eigenvalue of the dirichlet laplacian among sets with given volume in this paper we prove a sharp quantitative enhancement of this result thus confirming a conjecture by nadirashvili and bhattacharya weitsman more generally the result applies to every optimal poincare sobolev constant for the embeddings w 1 2 0 omega hookrightarrow l q omega

differential space time modulation space time coding and modulation exploit the presence of multiple transmit antennas to improve the performance on multipath radio channels thus far most work on space time coding has assumed that perfect channel estimates are available at the receiver in certain situations however it may be difficult or costly to estimate the channel accurately in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver we propose a general approach to differential modulation for multiple transmit antennas based on group codes this approach ran be applied to any number of transmit and receive antennas and any signal constellation we also derive low complexity differential receivers error bounds and modulator design criteria which we use to construct optimal differential modulation schemes for two transmit antennas these schemes can be demodulated with or without channel estimates this permits the receiver to exploit channel estimates when they are available the performance degrades by approximately 3 db when estimates are not available

limit theorems for monolayer ballistic deposition in the continuum we consider a deposition model in which balls rain down at random towards a 2 dimensional surface roll downwards over existing adsorbed balls are adsorbed if they reach the surface and discarded if not we prove a spatial law of large numbers and central limit theorem for the ultimate number of balls adsorbed onto a large toroidal surface and also for the number of balls adsorbed on the restriction to a large region of an infinite surface

spectral optimization for the stekloff laplacian the stability issue abstract we consider the problem of minimizing the first non trivial stekloff eigenvalue of the laplacian among sets with given measure we prove that the brock weinstock inequality asserting that optimal shapes for this spectral optimization problem are balls can be improved by means of a sharp quantitative stability estimate this result is based on the analysis of a certain class of weighted isoperimetric inequalities already proved in betta et al 1999 2 we provide some new sharp quantitative versions of these achieved by means of a suitable calibration technique

capacity and principal eigenvalues the method of enlargement of obstacles revisited we describe a coarse graining method which provides lower bounds on the principal dirichlet eigenvalue of the laplacian in regions receiving small obstacles and sharpens the previous method of enlargement of obstacles based on a quantitative wiener criterion one replaces the actual obstacles by obstacles of a much larger size controls on the shift of principal eigenvalues and capacity estimates on the locus where the wiener criterion breaks down are derived the results are written in a self contained fashion

robust multidimensional matched subspace classifiers based on weighted least squares we propose and design two classes of robust subspace classifiers for classification of multidimensional signals our classifiers are based on robust m estimators and the least median of squares principle and we show that they may be unified as iterated reweighted oblique subspace classifiers the performance of the proposed classifiers are demonstrated by two examples noncoherent detection of space time frequency shift keying signals and shape classification of partially occluded two dimensional 2 d objects in both cases the proposed robust subspace classifiers outperform the conventional subspace classifiers

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

coverage processes on spheres and condition numbers for linear programming this paper has two agendas firstly we exhibit new results for coverage processes let p n m alpha be the probability that n spherical caps of angular radius alpha in s m do not cover the whole sphere s m we give an exact formula for p n m alpha in the case alpha in pi 2 pi and an upper bound for p n m alpha in the case alpha in 0 pi 2 which tends to p n m pi 2 when alpha to pi 2 in the case alpha in 0 pi 2 this yields upper bounds for the expected number of spherical caps of radius alpha that are needed to cover s m secondly we study the condition number mathscr c a of the linear programming feasibility problem exists x in mathbb r m 1 ax le0 x ne0 where a in mathbb r n times m 1 is randomly chosen according to the standard normal distribution we exactly determine the distribution of mathscr c a conditioned to a being feasible and provide an upper bound on the distribution function in the infeasible case using these results we show that mathbf e ln mathscr c a le2 ln m 1 3 31 for all n m the sharpest bound for this expectancy as of today both agendas are related through a result which translates between coverage and condition

grassmannian packings from operator reed muller codes this paper introduces multidimensional generalizations of binary reed muller codes where the codewords are projection operators and the corresponding subspaces are widely separated with respect to the chordal distance on grassmannian space parameters of these grassmannian packings are derived and a low complexity decoding algorithm is developed by modifying standard decoding algorithms for binary reed muller codes the subspaces are associated with projection operators determined by pauli matrices appearing in the theory of quantum error correction and this connection with quantum stabilizer codes may be of independent interest the grassmannian packings constructed here find application in noncoherent wireless communication with multiple antennas where separation with respect to the chordal distance on grassmannian space guarantees closeness to the channel capacity it is shown that the capacity of the noncoherent multiple input multiple output mimo channel at both low and moderate signal to noise ratio snr under the constraint that only isotropically distributed unitary matrices are used for information transmission is closely approximated by these packings

a novel signaling scheme for blind unique identification of alamouti space time block coded channel in this paper we present a simple signaling scheme to blindly and uniquely identify the alamouti space time block coded channel first under a noise free environment and then under a complex gaussian noise environment in which pth and qth order statistics p and q are coprime of the received signals are available in both cases closed form solutions to determine the channel coefficients are obtained by exploiting specific properties of the alamouti space time block code stbc and the linear diophantine equation theory under gaussian noise when the length of the received data is finite we propose to use the semidefinite relaxation sdr algorithm to approximate maximum likelihood ml detection so that the joint estimation of the channel and symbols can be efficiently implemented simulation results show that while other existing blind methods fail our signaling scheme works well

systematic design of unitary space time constellations we propose a systematic method for creating constellations of unitary space time signals for multiple antenna communication links unitary space time signals which are orthonormal in time across the antennas have been shown to be well tailored to a rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients the signals can achieve low probability of error by exploiting multiple antenna diversity because the fading coefficients are not known the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum euclidean distance norm our construction begins with the first signal in the constellation an oblong complex valued matrix whose columns are orthonormal and systematically produces the remaining signals by successively rotating this signal in a high dimensional complex space this construction easily produces large constellations of high dimensional signals we demonstrate its efficacy through examples involving one two and three transmitter antennas

the supercritical phase of percolation is well behaved we prove a general result concerning the critical probabilities of subsets of a lattice l it is a consequence of this result that the critical probability of a percolation process on l equals the limit of the critical probability of a slice of l as the thickness of the slice tends to infinity this verification of one of the standard hypotheses of the subject settles many questions concerning supercritical percolation

optimal signaling schemes and capacities of non coherent correlated miso channels under per antenna power constraints this paper investigates the optimal signaling schemes and capacities of non coherent correlated multiple input single output miso channels in fast rayleigh fading we consider both channels under per antenna power constraints as well as channels under joint per antenna and sum power constraints for per antenna power constraint channels we first establish the convex and compact properties of the feasible sets and demonstrate the existence of optimal input distribution and the uniqueness of optimal effective magnitude input distribution by exploiting the solutions of a quadratic optimization problem we show that the kuhn tucker condition on the optimal inputs can be simplified to a single dimension as a result we can apply the identity theorem to show the discrete and finite nature of the optimal effective magnitude distribution with a mass point located at the origin by using this distribution we then construct a finite and discrete optimal input vector distribution the use of this input allows us to determine the capacity gain of miso over siso via the phase solutions of a constrained quadratic optimization problem on a sphere which can be obtained using a proposed penalized optimization algorithm we also extend the results to miso channels subject to the joint per antenna and sum power constraints under this consideration it is shown that not all per antenna constraints are active while the finiteness and discreteness of the optimal effective magnitude and the optimal input vector distributions still hold the optimal phases and the optimal power allocation among the transmit antennas need to be determined simultaneously via a quadratic optimization problem under inequality constraints these solutions can finally be used to obtain the miso capacity gain

multiple antenna signaling over fading channels with estimated channel state information performance analysis multiple antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation in this paper we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance we consider a training based multiple antenna system that reserves a portion of time to sound the channel training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver no channel state information csi is assumed at the transmitter we present a new framework to analyze training based multiple antenna systems by introducing an equivalent system model that specifies the channel by the estimated and hence known channel coefficients and an uncorrelated data dependent multiplicative noise we derive the maximum likelihood ml detector and highlight its behavior in the limiting cases of perfect csi and no csi and its relation to several mismatched detectors we deduce new exact expressions and chernoff bounds of the pairwise error probability pep used to assess word error and bit error rate bounds for ml and mismatched detection finally we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes and present numerical results

isotropic fading vector broadcast channels the scalar upper bound and loss in degrees of freedom we propose a scalar upper bound on the capacity region of the isotropic fading vector broadcast channel in terms of the capacity region of a scalar fading broadcast channel the scalar upper bound is applicable to the broad class of isotropic fading broadcast channels regardless of the distribution of the users channel magnitudes the distribution of the additive noise experienced by each user or the amount of channel knowledge available at the receiver using this upper bound we prove the optimality of the alamouti scheme in a broadcast setting extend the recent results on the capacity of nondegraded fading scalar broadcast channels to nondegraded fading vector broadcast channels and determine the capacity region of a fading vector gaussian broadcast channel with channel magnitude feedback we also provide an example of a rayleigh fading broadcast channel with no channel state information available to the receiver csir where the bound on the capacity region obtained by a naive application of the scalar upper bound is provably loose because it fails to account for the additional loss in degrees of freedom due to lack of channel knowledge at the receiver a tighter upper bound is obtained by separately accounting for the loss in degrees of freedom due to lack of csir before applying the scalar upper bound

andre quillen cohomology and rational homotopy of function spaces we develop a simple theory of andre quillen cohomology for commutative differential graded algebras over a field of characteristic zero we then relate it to the homotopy groups of function spaces and spaces of homotopy self equivalences of rational nilpotent cw complexes this puts certain results of sullivan in a more conceptual framework

surface order large deviations for ising potts and percolation models we derive uniform surface order large deviation estimates for the block magnetization in finite volume ising or potts models with plus or free or a combination of both boundary conditions in the phase coexistence regime ford 3 the results are valid up to a limit of slab thresholds conjectured to agree with the critical temperature our arguments are based on the renormalization of the random cluster model withq 1 andd 3 and on corresponding large deviation estimates for the occurrence in a box of a largest cluster with density close to the percolation probability the results are new even for the case of independent percolation q 1 as a byproduct of our methods we obtain further results in the fk model concerning semicontinuity inp andq of the percolation probability the second largest cluster in a box and the tail of the finite cluster size distribution

localization for random walks among random obstacles in a single euclidean ball place an obstacle with probability 1 p independently at each vertex of mathbb z d and run a simple random walk before hitting one of the obstacles for d ge 2 and p strictly above the critical threshold for site percolation we condition on the environment where the origin is contained in an infinite connected component free of obstacles and we show that for environments with probability tending to one as n rightarrow infty there exists a unique discrete euclidean ball of volume d log 1 p n asymptotically such that the following holds conditioned on survival up to time n we have that at any time t in epsilon n n n for some epsilon n rightarrow n rightarrow infty 0 with probability tending to one the simple random walk is in this ball this work relies on and substantially improves a previous result of the authors on localization in a region of volume poly logarithmic in n for the same problem

central limit theorem for exponentially quasi local statistics of spin models on cayley graphs central limit theorems for linear statistics of lattice random fields including spin models are usually proven under suitable mixing conditions or quasi associativity many interesting examples of spin models do not satisfy mixing conditions and on the other hand it does not seem easy to show central limit theorem for local statistics via quasi associativity in this work we prove general central limit theorems for local statistics and exponentially quasi local statistics of spin models on discrete cayley graphs with polynomial growth further we supplement these results by proving similar central limit theorems for random fields on discrete cayley graphs taking values in a countable space but under the stronger assumptions of alpha mixing for local statistics and exponential alpha mixing for exponentially quasi local statistics all our central limit theorems assume a suitable variance lower bound like many others in the literature we illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology statistical physics and random networks examples of clustering spin models include quasi associated spin models with fast decaying covariances like the off critical ising model level sets of gaussian random fields with fast decaying covariances like the massive gaussian free field and determinantal point processes with fast decaying kernels examples of local statistics include intrinsic volumes face counts component counts of random cubical complexes while exponentially quasi local statistics include nearest neighbour distances in spin models and betti numbers of sub critical random cubical complexes

asymptotic survival probabilities in the random saturation process we consider a model of diffusion in random media with a two way coupling i e a model in which the randomness of the medium influences the diffusing particles and where the diffusing particles change the medium in this particular model particles are injected at the origin with a time dependent rate and diffuse among random traps each trap has a finite random depth so that when it has absorbed a finite random number of particles it is saturated and it no longer acts as a trap this model comes from a problem of nuclear waste management however a very similar model has been studied recently by gravner and quastel with different tools hydrodynamic limits we compute the asymptotic behavior of the probability of survival of a particle born at some given time both in the annealed and quenched cases and show that three different situations occur depending on the injection rate for weak injection the typical survival strategy of the particle is as in sznitman and the asymptotic behavior of this survival probability behaves as if there was no saturation effect for medium injection rate the picture is closer to that of internal dla as given by lawler bramson and griffeath for large injection rates the picture is less understood except in dimension one

a central limit theorem with applications to percolation epidemics and boolean models suppose x x x x zd is a white noise process and h b defined for finite subsets b of z d is determined in a stationary way by the restriction of x to b using a martingale approach we prove a central limit theorem clt for h as b becomes large subject to h satisfying a stabilization condition the effect of changing x x at a single site needs to be local this clt is then applied to component counts for percolation and boolean models to the size of the big cluster for percolation on a box and to the final size of a spatial epidemic

compactness via symmetrization consider two types of translation invariant functionals i and j on rm and a sequence of functions fn whose corresponding symmetric rearrangements f n are convergent we show that fn themselves converge up to translations if either limn i fn limn i fn or limn j fn limn j fn these compactness results lead to applications in variational problems and stability problems in stellar dynamics

localization of a two dimensional random walk with an attractive path interaction we consider an ordinary symmetric continuous time random walk on the two dimensional lattice mathbb z 2 the distribution of the walk is transformed by a density which discounts exponentially the number of points visited up to time t this introduces a self attracting interaction of the paths we study the asymptotic behavior for t rightarrow infty it turns out that the displacement is asymptotically of order t 1 4 the main technique for proving the result is a refined analysis of large deviation probabilities a partial discussion is given also for higher dimensions

generalized quadratic receivers for unitary space time modulation over rayleigh fading channels we propose the generalized quadratic receivers gqrs for unitary space time modulation over flat rayleigh fading channels the gqrs realize the performance improvement potential known to be approximately 2 4 db between the quadratic receiver qr and the coherent receiver cr by performing channel estimation without the help of additional training signals that consume additional bandwidth they are designed for various unitary space time constellations ustc in which signal matrices may or may not contain explicit inherent training blocks and may be orthogonal or nonorthogonal to one another as the channel memory span exploited for channel estimation increases the error probability of the gqrs reduces from that of the qr to that of the cr the gqrs work well for both slow and fast fading channels and the performance improvement increases as the channel fade rate decreases for a class of ustc with the orthogonal design structure the gqr is simplified to a form whose complexity can be less than the complexity of the qr or even that of the simplified form of the qr

confinement of brownian motion among poissonian obstacles in ℝ d d 3 consider brownian motion among random obstacles obtained by translating a fixed compact nonpolar subset of d d 1 at the points of a poisson cloud of constant intensity v 0 assume that brownian motion is absorbed instantaneously upon entering the obstacle set in szn conf sznitman has shown that in d 2 conditionally on the event that the process does not enter the obstacle set up to time t the probability that brownian motion remains within distance t1 4 from its starting point is going to 1 as t goes to infinity we show that the same result holds true for d 3 with t1 4 replaced by t1 d 2 the proof is based on sznitmans refined method of enlargement of obstacles 10 as well as on a quantitative isoperimetric inequality due to hall 4

mathematics of random growing interfaces we establish a thermodynamic limit and gaussian fluctuations for the height and surface width of the random interface formed by the deposition of particles on surfaces the results hold for the standard ballistic deposition model as well as the surface relaxation model in the off lattice setting the results are proved with the aid of general limit theorems for stabilizing functionals of marked poisson point processes

space time frequency shift keying frequency shift keying fsk is a popular modulation scheme in power limited communication links this paper introduces space time fsk st fsk which does not require any channel state information at the transmitter and the receiver as in conventional noncoherent fsk st fsk can be viewed as a special unitary st modulation design however st fsk has a number of advantages over existing unitary st modulation designs st fsk is easier to design and enjoys lower decoding complexity furthermore st fsk guarantees full diversity finally st fsk can be adopted in the digital as well as in the analog domain and merges very naturally with frequency hopping multiple access as expected all these advantages come at the cost of a decrease in spectral efficiency

leveraging coherent space time codes for noncoherent communication via training training codes are introduced for the multiple antenna noncoherent multiple block rayleigh fading channel in which the fading coefficients which are constant over a fixed number of dimensions coherence interval for each block and then change independently to a new realization are known neither at the transmitter nor at the receiver each codeword of a training code consists of a part known to the receiver used to form a minimum mean squared error mmse estimate of the channel and a part that contains codeword s of a space time block or trellis code designed for the coherent channel in which the receiver has perfect knowledge of the channel the channel estimate is used as if it were error free for decoding the information bearing part of the training codeword training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable conditions for which the estimator detector e d receiver is equivalent to the optimal noncoherent receiver are established a key performance analysis result of this paper is that the training codes when decoded with the e d receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code in some cases the performance of training codes can be measured relative to coherent reception via training efficiency which is then optimized over the energy allocation between the training and data phases in the limit of increasing block lengths training codes always achieve the performance of coherent reception the examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available even though the latter require exponential decoding complexity

topological andre quillen cohomology and e andre quillen cohomology abstract we show that the andre quillen cohomology of an e simplicial algebra with arbitrary coefficients and the topological andre quillen cohomology of an e ring spectrum with eilenberg mac lane coefficients may be calculated as the andre quillen cohomology of an associated e differential graded algebra

spectrum bottom and largest vacuity the paper considers a scalar second order elliptic operator with a non negative random potential term v x x w x x 0 corresponding to a poisson cloud x of soft obstacles the operator acts on functions vanishing outside a large cubic open box rq 0 r r d d d 2 the paper develops a method of estimating from below the spectrum bottom of the operator through the volume of the largest connected set that can be made of smaller blocks containing relatively few obstacles in the case of constant coefficients the principal eigenvalue v r of v in r 0 is shown to satisfy with high probability the estimate where is the infimum of principal value of operator with zero potential term v 0 under the dirichlet condition on the boundary of a regular set of volume not exceeding one

fluctuations of principal eigenvalues and random scales we investigate the principal dirichlet eigenvalue of the laplacian with soft poissonian obstacles in large boxes of d 2 with the help of our recent version of the method of enlargement of obstacles 18 we derive quantitative confidence intervals for these eigenvalues we also provide less quantitative estimates which however point out the correct size of fluctuations and indicate a stiffness in their behavior in the two dimensional case we derive geometric controls which relate these eigenvalues to certain empty circular droplets our results also have natural applications to the study of the location of minima of certain intermittent random variational problems motivated by 13 17

differential unitary space time modulation we present a framework for differential modulation with multiple antennas across a continuously fading channel where neither the transmitter nor the receiver knows the fading coefficients the framework can be seen as a natural extension of standard differential phase shift keying commonly used in single antenna unknown channel systems we show how our differential framework links the unknown channel system with a known channel system and we develop performance design criteria as a special ease we introduce a class of diagonal signals where only one antenna is active at any time and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error

distribution of size structure and number of vacant regions in a high intensity mosaic a mosaic is formed by centring independent and identically distributed random sets at points of a poisson process in euclidean space we derive high intensity approximations to the distributions of size structure and number of uncovered regions in a mosaic a limit theorem is proved for vacancy and leads to a general approximation to the probability that a given region is completely covered by random shapes

lifshitz tails for random schrodinger operators with negative singular poisson potential we develop a method of asymptotic study of the integrated density of states ids n e of a random schrodinger operator with a non positive attractive poisson potential the method is based on the periodic approximations of the potential instead of the dirichlet neumann bracketing used before this allows us to derive more precise bounds for the rate of approximations of the ids by the ids of respective periodic operators and to obtain rigorously for the first time the leading term of log n e as e for the poisson random potential with a singular single site impurity potential in particular for the screened coulomb impurities dislocations etc

the central limit theorem for supercritical oriented percolation in two dimensions we consider the cardinality of supercritical oriented bond percolation in two dimensions we show that whenever the the origin is conditioned to percolate the process appropriately normalized converges asymptotically in distribution to the standard normal law this resolves a longstanding open problem pointed out to in several instances in the literature the result applies also to the continuous time analog of the process viz the basic one dimensional contact process we also derive general random indices central limit theorems for associated random variables as byproducts of our proof

derived koszul duality and tq homology completion of structured ring spectra abstract working in the context of symmetric spectra we consider algebraic structures that can be described as algebras over an operad o topological quillen homology or tq homology is the spectral algebra analog of quillen homology and stabilization working in a framework for homotopical descent the associated tq homology completion map appears as the unit map of an adjunction comparing the homotopy categories of o algebra spectra with coalgebra spectra over the associated comonad via tq homology we prove that this adjunction between homotopy categories can be turned into an equivalence by replacing o algebras with the full subcategory of 0 connected o algebras we also construct the spectral algebra analog of the unstable adams spectral sequence that starts from the tq homology groups tq x of an o algebra x and prove that it converges strongly to x when x is 0 connected

percolation of poisson sticks on the plane we consider a percolation model on the plane which consists of 1 dimensional sticks placed at points of a poisson process onr 2 each stick having a random but bounded length and a random direction the critical probabilities are defined with respect to the occupied clusters and vacant clusters and they are shown to be equal the equality is shown through a pivotal cell argument using a version of the russo seymour welsh theorem which we obtain for this model

communication on the grassmann manifold a geometric approach to the noncoherent multiple antenna channel we study the capacity of multiple antenna fading channels we focus on the scenario where the fading coefficients vary quickly thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver we use a noncoherent block fading model proposed by marzetta and hochwald see ibid vol 45 p 139 57 1999 the model does not assume any channel side information at the receiver or at the transmitter but assumes that the coefficients remain constant for a coherence interval of length t symbol periods we compute the asymptotic capacity of this channel at high signal to noise ratio snr in terms of the coherence time t the number of transmit antennas m and the number of receive antennas n while the capacity gain of the coherent multiple antenna channel is min m n bits per second per hertz for every 3 db increase in snr the corresponding gain for the noncoherent channel turns out to be m 1 m t bits per second per hertz where m min m n t 2 the capacity expression has a geometric interpretation as sphere packing in the grassmann manifold

brownian confinement and pinning in a poissonian potential ii we study the behavior of ad dimensional brownian motion in a soft repulsive poissonian potential over long time intervals 0 t we introduce certaint and configuration dependent scales which grow almost linearly witht for typical configurations with probability tending to 1 ast goes to the size of displacements of the process is bounded above by these scales confinement effect the proof involves calculations beyond leading order to this end we use a coarse grained picture of the environment method of enlargement of obstacles and of the path a backbone of excursions between clearings and forest parts in the environment these coarse grained pictures are also used in the sequel 11 to the present article when proving the pinning effect