absorbing boundary in one dimensional anomalous transport in this paper we study the space time probability distribution q x t of a random walk subject to an absorbing boundary at the origin x 0 for motion controlled by l evy flights and l evy walks characterized by the exponent ensuremath gamma we find that the method of images usually applicable to brownian motion may break down for l evy processes we calculate the distribution q x t to be at xg0 after time tg0 having started at the origin assuming that the boundary is effective at time tg0 we show that q x t depends on the details of the underlying process q x t ensuremath sim mathit x ensuremath gamma 2 mathit t 1 1 ensuremath gamma 1 ensuremath le ensuremath gamma ensuremath le 2 for small x while total survival is independent of the spatial realization of motion and displays a universal behavior we also discuss the related smoluchowski boundary condition problem

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

vicious walks with long range interactions the asymptotic behavior of the survival or reunion probability of vicious walks with short range interactions is generally well studied in many realistic processes however walks interact with a long ranged potential that decays in d dimensions with distance r as r ensuremath d ensuremath ensuremath sigma we employ methods of renormalized field theory to study the effect of such long range interactions we calculate the exponents describing the decay of the survival probability for all values of parameters ensuremath sigma and d to first order in the double expansion in ensuremath epsilon 2 ensuremath d and ensuremath delta 2 ensuremath d ensuremath ensuremath sigma we show that there are several regions in the ensuremath sigma text ensuremath d plane corresponding to different scalings for survival and reunion probabilities furthermore we calculate the leading logarithmic corrections

non intersecting paths random tilings and random matrices we investigate certain measures induced by families of non intersecting paths in domino tilings of the aztec diamond rhombus tilings of an abc hexagon a dimer model on a cylindrical brick lattice and a growth model the measures obtained e g the krawtchouk and hahn ensembles have the same structure as the eigenvalue measures in random matrix theory like gue which can in fact can be obtained from non intersecting brownian motions the derivations of the measures are based on the karlin mcgregor or lindstrom gessel viennot method we use the measures to show some asymptotic results for the models

fractional laplacian in bounded domains the fractional laplacian operator ensuremath ensuremath ensuremath delta ensuremath alpha 2 appears in a wide class of physical systems including l evy flights and stochastic interfaces in this paper we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval the implementation of boundary conditions is justified by appealing to two physical models namely hopping particles and elastic springs the eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions some analytical results concerning the structure of the eigenvalue spectrum are also obtained

levy flights on the half line we study the probability distribution function pdf of the position of a levy flight of index 0 2 in the presence of an absorbing wall at the origin the solution of the associated fractional fokker planck equation can be constructed using a perturbation scheme around the brownian solution corresponding to 2 as an expansion in e 2 we obtain an explicit analytical solution exact at the first order in e which allows us to conjecture the precise asymptotic behavior of this pdf including the first subleading corrections for any careful numerical simulations as well as an exact computation for 1 confirm our conjecture

first passage and arrival time densities for levy flights and the failure of the method of images we discuss the first passage time problem in the semi infinite interval for homogeneous stochastic markov processes with levy stable jump length distributions x l x 1 x l namely levy flights lfs in particular we demonstrate that the method of images leads to a result which violates a theorem due to sparre andersen according to which an arbitrary continuous and symmetric jump length distribution produces a first passage time density fptd governed by the universal long time decay t 3 2 conversely we show that for lfs the direct definition known from gaussian processes in fact defines the probability density of first arrival which for lfs differs from the fptd our findings are corroborated by numerical results

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

vicious levy flights we study the statistics of encounters of levy flights by introducing the concept of vicious levy flights distinct groups of walkers performing independent levy flights with the process terminating upon the first encounter between walkers of different groups we show that the probability that the process survives up to time t decays as t at late times we compute up to the second order in e expansion where e d is the levy exponent and d is the spatial dimension for d we find the exponent of the logarithmic decay exactly theoretical values of the exponents are confirmed by numerical simulations our results indicate that walkers with smaller values of survive longer and are therefore more effective at avoiding each other

communication over mimo x channels interference alignment decomposition and performance analysis in a multiple antenna system with two transmitters and two receivers a scenario of data communication known as the x channel is studied in which each receiver receives data from both transmitters in this scenario it is assumed that each transmitter is unaware of the other transmitter s data noncooperative scenario this system can be considered as a combination of two broadcast channels from the transmitters points of view and two multiple access channels from the receivers points of view taking advantage of both perspectives two signaling schemes for such a scenario are developed in these schemes some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple antenna broadcast subchannels or two noninterfering multiple antenna multiple access subchannels the main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain mg it is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable mg in particular it is shown that in some specific cases the achieved mg is the same as the mg of the system if full cooperation is provided either between the transmitters or between the receivers in the second part of the paper it is shown that by using mixed design schemes rather than decomposition schemes and taking the statistical properties of the interference terms into account the power offset of the system can be improved the power offset represents the horizontal shift in the curve of the sum rate versus the total power in decibels

universal first passage properties of discrete time random walks and levy flights on a line statistics of the global maximum and records abstract in these lecture notes i will discuss the universal first passage properties of a simple correlated discrete time sequence x 0 0 x 1 x 2 x n up to n steps where x i represents the position at step i of a random walker hopping on a continuous line by drawing independently at each time step a random jump length from an arbitrary symmetric and continuous distribution it includes e g the levy flights i will focus on the statistics of two extreme observables associated with the sequence i its global maximum and the time step at which the maximum occurs and ii the number of records in the sequence and their ages i will demonstrate how the universal statistics of these observables emerge as a consequence of pollaczek spitzer formula and the associated sparre andersen theorem

chern simons theory matrix integrals and perturbative three manifold invariants the universal perturbative invariants of rational homology spheres can be extracted from the chern simons partition function by combining perturbative and nonperturbative results we spell out the general procedure to compute these invariants and we work out in detail the case of seifert spaces by extending some previous results of lawrence and rozansky the chern simons partition function with arbitrary simply laced group for these spaces is written in terms of matrix integrals the analysis of the perturbative expansion amounts to the evaluation of averages in a gaussian ensemble of random matrices as a result explicit expressions for the universal perturbative invariants of seifert homology spheres up to order five are presented

random vicious walks and random matrices a lock step walk is a one dimensional integer lattice walk in discrete time suppose that initially there are infinitely many walkers on the nonnegative even integer sites at each moment of time every walker moves either to its left or to its right with equal probability the only constraint is that no two walkers can occupy the same site at the same time hence we describe the walk as vicious it is proved that as time tends to infinity a certain limiting conditional distribution of the displacement of the leftmost walker is identical to the limiting distribution of the scaled largest eigenvalue of a random goe matrix goe tracy widom distribution the proof is based on the bijection between path configurations and semistandard young tableaux established recently by guttmann owczarek and viennot the distribution of semistandard young tableaux is analyzed using the hankel determinant expression for the probability obtained from the work of rains and the author the asymptotics of the hankel determinant are then obtained by applying the deift zhou steepest descent method to the riemann hilbert problem for the related orthogonal polynomials 2000 john wiley sons inc

erratum stabilization of solutions to nonlinear schrodinger equations the proof of lemma 5 2 in 1 contains several mistakes nevertheless thestatement is correct and is proven in an elementary fashion correctly this time in 3 lemma 2 4 which is in this issue of the journal in the proof of corollary 3 2 in 1 we misquoted from kato s textbook on per turbation theory in fact it is not true that as asserted in 1 corollary 3 2 followsfrom lemma 3 1 however corollary 3 2 of 1 is a consequence of proposition 3 1in 2 or under more general hypotheses that allow eigenvalues embedded in thecontinuous spectrum and for space dimension 3 proposition 4 1 in 3

o connell s process as a vicious brownian motion vicious brownian motion is a diffusion scaling limit of fisher s vicious walk model which is a system of brownian particles in one dimension such that if two motions meet they kill each other we consider the vicious brownian motions conditioned never to collide with each other and call it noncolliding brownian motion this conditional diffusion process is equivalent to the eigenvalue process of the hermitian matrix valued brownian motion studied by dyson j math phys 3 1191 1962 recently o connell ann probab to be published introduced a generalization of the noncolliding brownian motion by using the eigenfunctions the whittaker functions of the quantum toda lattice in order to analyze a directed polymer model in 1 1 dimensions we consider a system of one dimensional brownian motions with a long ranged killing term as a generalization of the vicious brownian motion and construct the o connell process as a conditional process of the killing brownian motions to survive forever

on asymptotic stability in energy space of ground states of nls in 1d abstract we transpose work by t mizumachi to prove smoothing estimates for dispersive solutions of the linearization at a ground state of a nonlinear schrodinger equation nls in 1d as an application we extend to dimension 1d a result on asymptotic stability of ground states of nls proved by cuccagna and mizumachi for dimensions 3

a critical center stable manifold for schrodinger s equation in three dimensions consider the focusing critical semilinear schrodinger equation in it admits an eight dimensional manifold of special solutions called ground state solitons we exhibit a codimension 1 critical real analytic manifold of asymptotically stable solutions of 0 1 in a neighborhood of the soliton manifold we then show that is center stable in the dynamical systems sense of bates and jones and globally in time invariant solutions in are asymptotically stable and separate into two asymptotically free parts that decouple in the limit a soliton and radiation conversely in a general setting any solution that stays close to the soliton manifold for all time is in the proof uses the method of modulation new elements include a different linearization and an endpoint strichartz estimate for the time dependent linearized equation the proof also uses the fact that the linearized hamiltonian has no nonzero real eigenvalues or resonances this has recently been established in the case treated here of the focusing cubic nls in by the work of marzuola and simpson and costin huang and schlag 2012 wiley periodicals inc

maximum distributions of bridges of noncolliding brownian paths one dimensional brownian motion starting from the origin at time t 0 conditioned to return to the origin at time t 1 and to stay positive during time interval 0 t 1 is called the bessel bridge with duration 1 we consider an n particle system of such bessel bridges conditioned never to collide with each other in 0 t 1 which is the continuum limit of the vicious walk model in watermelon configuration with a wall distributions of maximum values of paths attained in the time interval t epsilon 0 1 are studied to characterize the statistics of random patterns of the repulsive paths on the spatiotemporal plane for the outermost path the distribution function of maximum value is exactly determined for general n we show that the present n path system of noncolliding bessel bridges is realized as the positive eigenvalue process of the 2nx2n matrix valued brownian bridge in the symmetry class c using this fact computer simulations are performed and numerical results on the n dependence of the maximum value distributions of the inner paths are reported the present work demonstrates that the extreme value problems of noncolliding paths are related to random matrix theory the representation theory of symmetry and number theory

maximal fermi walk configurations on the directed square lattice and standard young tableaux we consider configurations of n walkers each of which starts at the origin of a directed square lattice and makes the same number t of steps from node to node along the edges of the lattice bose walkers are not allowed to cross but can share edges fermi walk configurations must satisfy the additional constraint that no two walkers traverse the same path since for given t there are only a finite number of t step paths there is a limit nmax on the number of walkers allowed by the fermi condition the value of nmax is determined for six types of boundary conditions the number of fermi configurations of nmax walkers is also determined using a bijection to standard young tableaux in four cases there is no constraint on the endpoints of the walks and the relevant tableaux are shifted

a centre stable manifold for the focussing cubic nls in mathbb r 1 3 consider the focussing cubic nonlinear schrodinger equation in mathbb r 3 i psi t delta psi psi 2 psi quad 0 1 it admits special solutions of the form eit where phi in mathcal s mathbb r 3 is a positive 0 solution of delta phi alpha phi phi 3 quad 0 2 the space of all such solutions together with those obtained from them by rescaling and applying phase and galilean coordinate changes called standing waves is the 8 dimensional manifold that consists of functions of the form e i v cdot gamma phi cdot y alpha we prove that any solution starting sufficiently close to a standing wave in the sigma w 1 2 mathbb r 3 cap x 1 l 2 mathbb r 3 norm and situated on a certain codimension one local lipschitz manifold exists globally in time and converges to a point on the manifold of standing waves furthermore we show that mathcal n is invariant under the hamiltonian flow locally in time and is a centre stable manifold in the sense of bates jones batjon the proof is based on the modulation method introduced by soffer and weinstein for the l2 subcritical case and adapted by schlag to the l2 supercritical case an important part of the proof is the keel tao endpoint strichartz estimate in mathbb r 3 for the nonselfadjoint schrodinger operator obtained by linearizing 0 1 around a standing wave solution all results in this paper depend on the standard spectral assumption that the hamiltonian mathcal h left begin array cc delta 2 phi cdot alpha 2 alpha quad phi cdot alpha 2 phi cdot alpha 2 quad delta 2 phi cdot alpha 2 alpha end array right quad 0 3 has no embedded eigenvalues in the interior of its essential spectrum infty alpha cup alpha infty

discrete polynuclear growth and determinantal processes we consider a discrete polynuclear growth png process and prove a functional limit theorem for its convergence to the airy process this generalizes previous results by prahofer and spohn the result enables us to express the f1 goe tracy widom distribution in terms of the airy process we also show some results and give a conjecture about the transversal fluctuations in a point to line last passage percolation problem furthermore we discuss a rather general class of measures given by products of determinants and show that these measures have determinantal correlation functions

perturbation theory for fractional brownian motion in presence of absorbing boundaries fractional brownian motion is a gaussian process x t with zero mean and two time correlations x t 1 x t 2 d t 1 2h t 2 2h t 1 t 2 2h where h with 0 h 1 is called the hurst exponent for h 1 2 x t is a brownian motion while for h 1 2 x t is a non markovian process here we study x t in presence of an absorbing boundary at the origin and focus on the probability density p x t for the process to arrive at x at time t starting near the origin at time 0 given that it has never crossed the origin it has a scaling form p x t t h r x t h our objective is to compute the scaling function r y which up to now was only known for the markov case h 1 2 we develop a systematic perturbation theory around this limit setting h 1 2 e to calculate the scaling function r y to first order in e we find that r y behaves as r y y as y 0 near the absorbing boundary while r y y exp y 2 2 as y with 1 4e o e 2 and 1 2e o e 2 our e expansion result confirms the scaling relation 1 h h proposed in zoia rosso and majumdar phys rev lett 102 120602 2009 we verify our findings via numerical simulations for h 2 3 the tools developed here are versatile powerful and adaptable to different situations

symmetry of matrix valued stochastic processes and noncolliding diffusion particle systems as an extension of the theory of dyson s brownian motion models for the standard gaussian random matrix ensembles we report a systematic study of hermitian matrix valued processes and their eigenvalue processes associated with the chiral and nonstandard random matrix ensembles in addition to the noncolliding brownian motions we introduce a one parameter family of temporally homogeneous noncolliding systems of the bessel processes and a two parameter family of temporally inhomogeneous noncolliding systems of yor s generalized meanders and show that all of the ten classes of eigenvalue statistics in the altland zirnbauer classification are realized as particle distributions in the special cases of these diffusion particle systems as a corollary of each equivalence in distribution of a temporally inhomogeneous eigenvalue process and a noncolliding diffusion process a stochastic calculus proof of a version of the harish chandra itzykson zuber formula of integral over unitary group is established

schur polynomials and biorthogonal random matrix ensembles the study of the average of schur polynomials over a stieltjes wigert ensemble has been carried out by dolivet and tierz j math phys 48 023507 2007 e print arxiv hep th 0609167 where it was shown that it is equal to quantum dimensions using the same approach we extend the result to the biorthogonal case we also study using the littlewood richardson rule some particular cases of the quantum dimension result finally we show that the notion of giambelli compatibility of schur averages introduced by borodin et al adv appl math 37 209 2006 e print arxiv math ph 0505021 also holds in the biorthogonal setting

matrices coupled in a chain i eigenvalue correlations the general correlation function for the eigenvalues of p complex hermitian matrices coupled in a chain is given as a single determinant for this we use a slight generalization of a theorem of dyson

an invariant set in energy space for supercritical nls in 1d we consider radial solutions of a mass supercritical monic nls and we prove the existence of a set which looks like a hypersurface in the space of finite energy functions invariant for the flow and formed by solutions which converge to ground states

first passage leapovers of levy flights and the proper formulation of absorbing boundary conditions an important open problem in the theory of levy flights concerns the analytically tractable formulation of absorbing boundary conditions although the nonlocal approach where the dynamical operators are given restrictions on their domain properties has yielded substantial insights regarding the statistics of first passage the resultant modifications to the dynamical equations hinder the detailed analysis possible in the absence of these nonlocal restrictions in this study it is demonstrated that using the first hit distribution related to the first passage leapover as the absorbing sink preserves the tractability of the dynamical equations for a particle undergoing levy flight in particular knowledge of the first hit distribution is sufficient to fully determine the first passage time and position density of the particle without requiring operator domain restrictions or numerical simulations in addition we report on the first hit and leapover properties of first passages and arrivals for levy flights of arbitrary skew parameter and extend these results to levy flights in a certain ubiquitous class of potentials satisfying an integral condition

stable manifolds for all monic supercritical focusing nonlinear schrodinger equations in one dimension keywords critical schrodinger equation stable manifolds modulation theory spectral theory klein gordon equations non linear schrodinger blow up rate standing waves nonintegrable equations invariant manifolds stability theory solitary waves ground states instability reference epfl article 155183doi 10 1090 s0894 0347 06 00524 8 record created on 2010 11 19 modified on 2017 05 12

asymptotic n soliton like solutions of the subcritical and critical generalized korteweg de vries equations we consider the generalized korteweg de vries equations ut uxx upx 0t x r inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i in the subcritical and critical cases p 2 3 4 or 5 let r j t x qc j x c j t x j where j 1 n be n soliton solutions of this equation with corresponding speeds 0 c 1 c 2 c n in this paper we construct a solution u t of the generalized korteweg de vries equation such that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i this solution behaves asymptotically as t as the sum of n solitons without loss of mass by dispersion this is an exceptional behavior indeed being given the parameters c j 1 j n x j 1 j n we prove uniqueness of such a solution in the integrable cases p 2 and 3 such solutions are explicitly known and their properties were extensively studied in the literature they are called n soliton solutions therefore the existence result is new only for the nonintegrable cases the uniqueness result is new for all cases

levy flights and random searches in this work we discuss some recent contributions to the random search problem our analysis includes superdiffusive levy processes and correlated random walks in several regimes of target site density mobility and revisitability we present results in the context of mean field like and closed form average calculations as well as numerical simulations we then consider random searches performed in regular lattices and lattices with defects and we discuss a necessary criterion for distinguishing true superdiffusion from correlated random walk processes we invoke energy considerations in relation to critical survival states on the edge of extinction and we analyze the emergence of levy behavior in deterministic search walks finally we comment on the random search problem in the context of biological foraging

families of vicious walkers we consider a generalization of the vicious walker problem in which n random walkers in rd are grouped into p families using field theoretic renormalization group methods we calculate the asymptotic behaviour of the probability that no pairs of walkers from different families have met up to time t for d 2 this is constant but for d 2 it decays as a power t which we compute to e2 in an expansion in e 2 d the second order term depends on the ratios of the diffusivities of the different families in two dimensions we find a logarithmic decay ln t and compute exactly

spectra of positive and negative energies in the linearized nls problem we study the spectrum of the linearized nls equation in three dimensions in association with the energy spectrum we prove that unstable eigenvalues of the linearized nls problem are related to negative eigenvalues of the energy spectrum while neutrally stable eigenvalues may have both positive and negative energies the nonsingular part of the neutrally stable essential spectrum is always related to the positive energy spectrum we derive bounds on the number of unstable eigenvalues of the linearized nls problem and study bifurcations of embedded eigenvalues of positive and negative energies we develop the l 2 scattering theory for the linearized nls operators and recover results of grillakis 5 with a fermi golden rule c

stationary states in two dimensional systems driven by bivariate levy noises systems driven by ensuremath alpha stable noises could be very different from their gaussian counterparts stationary states in single well potentials can be multimodal moreover a potential well needs to be steep enough in order to produce stationary states here it is demonstrated that two dimensional 2d systems driven by bivariate ensuremath alpha stable noises are even more surprising than their 1d analogs in 2d systems intriguing properties of stationary states originate not only due to heavy tails of noise pulses which are distributed according to ensuremath alpha stable densities but also because of properties of spectral measures consequently 2d systems are described by a whole family of langevin and fractional diffusion equations solutions of these equations bear some common properties but also can be very different it is demonstrated that also for 2d systems potential wells need to be steep enough in order to produce bounded states moreover stationary states can have local minima at the origin the shape of stationary states reflects symmetries of the underlying noise i e its spectral measure finally marginal densities in power law potentials also have power law asymptotics

differential equations for dyson processes we call a dyson process any process on ensembles of matrices in which the entries undergo diffusion we are interested in the distribution of the eigenvalues or singular values of such matrices in the original dyson process it was the ensemble of n n hermitian matrices and the eigenvalues describe n curves given sets x1 xm the probability that for each k no curve passes through xk at time k is given by the fredholm determinant of a certain matrix kernel the extended hermite kernel for this reason we call this dyson process the hermite process similarly when the entries of a complex matrix undergo diffusion we call the evolution of its singular values the laguerre process for which there is a corresponding extended laguerre kernel scaling the hermite process at the edge leads to the airy process which was introduced by prahofer and spohn as the limiting stationary process for a polynuclear growth model and in the bulk to the sine process scaling the laguerre process at the edge leads to the bessel process

construction of solutions to the l 2 critical kdv equation with a given asymptotic behaviour we consider the critical korteweg de vries equation ut uxx u x 0 t x r let rj t x qcj x xj cjt j 1 n be n soliton solutions to this equation denote u t the kdv linear group and let v h be with sufficient decay on the right that is 1 x0 v l for some 0 0 we construct a solution u t to the critical korteweg de vries equation such that lim t u t u t v n x j 1 rj t h1 0

a turbo fde technique for reduced cp sc based block transmission systems for conventional cyclic prefix cp assisted block transmission systems the cp length is selected on the basis of the expected maximum delay spread with regard to single carrier sc based block transmission implementations a full length cp is recommendable since it allows good performances through the use of simple frequency domain equalization fde techniques in this letter a soft decision directed correction sddc aided turbo fde technique is presented for reduced cp sc based block transmission systems using conventional frame structures the relations with some already known iterative fde techniques are established and a set of performance results is reported and discussed the advantages of the proposed approach are emphasized namely the possibility of approximately achieving besides the obvious bandwidth efficiency gain the maximum power efficiency gain that a strong cp reduction allows

record statistics of a strongly correlated time series random walks and levy flights we review recent advances on the record statistics of strongly correlated time series whose entries denote the positions of a random walk or a l evy flight on a line after a brief survey of the theory of records for independent and identically distributed random variables we focus on random walks during the last few years it was indeed realized that random walks are a very useful laboratory to test the effects of correlations on the record statistics we start with the simple one dimensional random walk with symmetric jumps both continuous and discrete and discuss in detail the statistics of the number of records as well as of the ages of the records i e the lapses of time between two successive record breaking events then we review the results that were obtained for a wide variety of random walk models including random walks with a linear drift continuous time random walks constrained random walks like the random walk bridge and the case of multiple independent random walkers finally we discuss further observables related to records like the record increments as well as some questions raised by physical applications of record statistics like the effects of measurement error and noise

iterative frequency domain detection for ia precoded mc cdma systems interference alignment ia is a promising technique that allows high capacity gains in interfering channels on the other hand iterative frequency domain detection receivers based on the ib dfe concept iterative block decision feedback equalization can efficiently exploit the inherent space frequency diversity of the mimo mc cdma systems in this paper we combine iterative ia precoding at the transmitter with ib dfe based processing at the receiver for mc cdma systems the receiver is designed in two steps first a linear filter is used to mitigate the inter user aligned interference and then an iterative frequency domain receiver is designed to efficiently separate the spatial streams in the presence of residual inter user aligned interference at the output of the filter the matrices for this non linear space frequency equalizer are obtained by minimizing the overall mean square error mse of all data streams at each subcarrier our receiver structure is explicitly designed taking into account the residual inter user interference allowing both an efficient separation of the spatial streams and a reduction in the number of iterations of the ia procedure we also propose a simple yet accurate analytical approach for obtaining the performance of the proposed receiver structure our scheme achieves the maximum degrees of freedom provided by the ia precoding while allowing an almost optimum space diversity gain with performance close to the matched filter bound mfb

polynuclear growth model with external source and random matrix model with deterministic source we present a random matrix interpretation of the distribution functions which have appeared in the study of the one dimensional polynuclear growth png model with external sources it is shown that the distribution goe2 which is defined as the square of the gaussian orthogonal ensemble goe tracy widom distribution can be obtained as the scaled largest eigenvalue distribution of a special case of a random matrix model with a deterministic source which have been studied in a different context previously compared to the original interpretation of the goe2 as the square of goe ours has an advantage in that it can also describe the transition from the gaussian unitary ensemble gue tracy widom distribution to the goe2 we further demonstrate that our random matrix interpretation can be obtained naturally by noting the similarity of the topology between a certain noncolliding brownian motion model and the multilayer png model with an external source this provides us with a multimatrix model interpretation of the multipoint height distributions of the png model with an external source

record statistics for multiple random walks we study the statistics of the number of records r n n for n identical and independent symmetric discrete time random walks of n steps in one dimension all starting at the origin at step 0 at each time step each walker jumps by a random length drawn independently from a symmetric and continuous distribution we consider two cases i when the variance ensuremath sigma 2 of the jump distribution is finite and ii when ensuremath sigma 2 is divergent as in the case of l evy flights with index 0l ensuremath mu l2 in both cases we find that the mean record number ensuremath langle r n n ensuremath rangle grows universally as ensuremath sim ensuremath alpha n sqrt n for large n but with a very different behavior of the amplitude ensuremath alpha n for ng1 in the two cases we find that for large n ensuremath alpha n ensuremath approx 2 sqrt mathrm ln n independently of ensuremath sigma 2 in case i in contrast in case ii the amplitude approaches to an n independent constant for large n ensuremath alpha n ensuremath approx 4 sqrt ensuremath pi independently of 0l ensuremath mu l2 for finite ensuremath sigma 2 we argue and this is confirmed by our numerical simulations that the full distribution of r n n sqrt n ensuremath 2 sqrt mathrm ln n sqrt mathrm ln n converges to a gumbel law as n ensuremath rightarrow ensuremath infty and n ensuremath rightarrow ensuremath infty in case ii our numerical simulations indicate that the distribution of r n n sqrt n converges for n ensuremath rightarrow ensuremath infty and n ensuremath rightarrow ensuremath infty to a universal nontrivial distribution independently of ensuremath mu we discuss the applications of our results to the study of the record statistics of 366 daily stock prices from the standard poor s 500 index