brownian motion with restoring drift micro canonical ensemble and the thermodynamic limit we take up the old problem of micro canonical conditioning in the context of diffusion starting with a potential the schrodinger operator with ground state is carried by a conjugation into the diffusion generator with invariant density the latter motion is made micro canonical by first conditioning the path to be periodic and then further conditioning on the empirical mean square or particle number the thermodynamics are then studied by taking while d remains fixed the problem in this form owes its inception to mckean vaninsky cite mv2 who obtained the following result for with they showed the same type of diffusion appears in the thermodynamic limit but with drift arising from the shifted potential being such that the limiting mean square equals d their method of proof predicts the same outcome for so long as d is smaller than the canonical mean square while if the matter was unresolved the purpose of this note is to show a type of phase transition takes place in this case the conditioning is overcome in the limit and one sees the original stationary diffusion on the line the proof employs an entropy inequality due to csiszar 1

characterization of talagrand s transport entropy inequalities in metric spaces we give a characterization of transport entropy inequalities in metric spaces as an application we deduce that such inequalities are stable under bounded perturbation holley stroock perturbation lemma

from concentration to logarithmic sobolev and poincare inequalities abstract we give a new proof of the fact that gaussian concentration implies the logarithmic sobolev inequality when the curvature is bounded from below and also that exponential concentration implies poincare inequality under null curvature condition our proof holds on non smooth structures such as length spaces and provides a universal control of the constants we also give a new proof of the equivalence between dimension free gaussian concentration and talagrand s transport inequality

cut set bound is loose for gaussian relay networks the cut set bound developed by cover and el gamal in 1979 has since remained the best known upper bound on the capacity of the gaussian relay channel we develop a new upper bound on the capacity of the gaussian primitive relay channel which is tighter than the cut set bound our proof uses gaussian measure concentration to establish geometric relations satisfied with high probability between the n letter random variables associated with a reliable code for communicating over this channel we then translate these geometric relations into new information inequalities that cannot be obtained with classical methods combined with a tensorization argument proposed by courtade and ozgur in 2015 our result also implies that the current capacity approximations for gaussian relay networks which have linear gap to the cut set bound in the number of nodes are order optimal and lead to a lower bound on the pre constant

efficient algorithms for computing sommerfeld integral tails sommerfeld integrals sis are ubiquitous in the analysis of problems involving antennas and scatterers embedded in planar multilayered media it is well known that the oscillating and slowly decaying nature of their integrands makes the numerical evaluation of the si real axis tail segment a very time consuming and computationally expensive task therefore si tails have to be specially treated in this paper we compare two recently developed techniques for their efficient numerical evaluation first a partition extrapolation method in which the integration then summation procedure is combined with a new version of the weighted averages wa extrapolation technique is summarized the previous variants of wa technique are also discussed then a review of double exponential de quadrature formulas for direct integration of the si tails is presented the efficient way of implementing the algorithms their pros and cons as well as comparisons of their performance are discussed in detail

multiparametric quantum gl 2 lie bialgebras quantum r matrices and non relativistic limits multiparametric quantum deformations of gl 2 are studied through a complete classification of gl 2 lie bialgebra structures from these the non relativistic limit leading to harmonic oscillator lie bialgebras is implemented by means of a contraction procedure new quantum deformations of gl 2 together with their associated quantum r matrices are obtained and other known quantizations are recovered and classified several connections with integrable models are outlined

coding theorems for a continuous time gaussian channel with feedback the main aim of the paper is to prove a coding theorem for a continuous time gaussian channel with feedback under an average power constraint in the case of discrete time the coding theorem for the feedback gaussian channel has been shown by cover and pombra 1989

a characterization of dimension free concentration in terms of transportation inequalities the aim of this paper is to show that a probability measure concentrates independently of the dimension like a gaussian measure if and only if it verifies talagrand s t 2 transportation cost inequality this theorem permits us to give a new and very short proof of a result of otto and villani generalizations to other types of concentration are also considered in particular one shows that the poincare inequality is equivalent to a certain form of dimension free exponential concentration the proofs of these results rely on simple large deviations techniques

bayesian methods and maximum entropy for ill posed inverse problems in this paper we study linear inverse problems where some generalized moments of an unknown positive measure are observed we introduce a new construction called the maximum entropy on the mean method mem which relies on a suitable sequence of finite dimensional discretized inverse problems its advantage is threefold it allows us to interpret all usual deterministic methods as bayesian methods it gives a very convenient way of taking into account prior information it also leads to new criteria for the existence question concerning the linear inverse problem which will be a starting point for the investigation of superresolution phenomena the key tool in this work is the large deviations property of some discrete random measure connected with the reconstruction procedure

measure concentration for euclidean distance in the case of dependent random variables let qn be a continuous density function in n dimensional euclidean space we think of qn as the density function of some random sequence xn with values in bbb r n for i 1 n let xi denote the collection of coordinates xi i i and let widebar x i denote the collection of coordinates xi i i we denote by q i x i bar x i the joint conditional density function of xi given widebar x i we prove measure concentration for qn in the case when for an appropriate class of sets i i the conditional densities q i x i bar x i as functions of xi uniformly satisfy a logarithmic sobolev inequality and ii these conditional densities also satisfy a contractivity condition related to dobrushin and shlosman s strong mixing condition

some inequalities for information divergence and related measures of discrimination inequalities which connect information divergence with other measures of discrimination or distance between probability distributions are used in information theory and its applications to mathematical statistics ergodic theory and other scientific fields we suggest new inequalities of this type often based on underlying identities as a consequence we obtain certain improvements of the well known pinsker inequality our study depends on two measures of discrimination called capacitory discrimination and triangular discrimination the discussion contains references to related research and comparison with other measures of discrimination e g ali silvey csiszar 1996 1966 divergences and in particular the hellinger distance

the weighted averages algorithm revisited the classic weighted averages wa algorithm for the evaluation of sommerfeld like integrals is reviewed and reappraised as a result a new version of the wa algorithm called generalized wa is introduced the new version can be considered as a generalization of the well established holder and cesaro means used to sum divergent series generalized wa exhibits a more compact formulation devoid of iterative and recursive steps and a wider range of applications it is more robust as it provides a unique formulation valid for monotonic and oscillating functions the implementation of the new version is easier and more economical in terms of basic operations preliminary numerical examples show that generalized wa also outperforms in terms of accuracy the classic wa algorithm which is currently recognized as the most competitive algorithm to evaluate sommerfeld integral tails

on two dimensional spectral realization reconstruction of a spectral density function from a finite set of covariances can be performed by maximizing an entropy functional the method of the maximum entropy on the mean is used for computing a discrete version of this spectral density and allows one to give a new interpretation of these reconstruction methods in fact the authors show that the choice of the entropy is directly related to a prior distribution in particular they consider processes on z sup 2 steepest descent procedures permit the numerical computation of discrete realizations for a wide class of entropies to ensure the nonnegativity of the solution related to the burg entropy they present a new algorithm based on a fixed point method and the yule walker equations to compute this solution then the solution of the dual problem is obtained as the limit of the trajectory of an ordinary differential equation

an on line universal lossy data compression algorithm via continuous codebook refinement ii optimality for phi mixing source models for pt i see ibid vol 42 no 3 p 803 21 1996 two versions of the gold washing data compression algorithm one with codebook innovation interval and the other with finitely many codebook innovations are considered the version of the gold washing algorithm with codebook innovation interval k is a variant of the gold washing algorithm such that the codebook is innovated once every k 1 source words during the process of encoding the entire source it is demonstrated that when this version of the gold washing algorithm is applied to encode a stationary spl phi mixing source the expected distortion performance converges to the distortion rate function of the source as the codebook length goes to infinity furthermore if the source to be encoded is a markov source or a finite state source then the corresponding sample distortion performance converges almost surely to the distortion rate function the version of the gold washing algorithm with finitely many codebook innovations is a variant of the gold washing algorithm in which after finitely many codebook innovations the codebook is held fixed and reused to encode the forthcoming source sequence block by block similar results are shown for this version of the gold washing algorithm in addition the convergence speed of the algorithm is discussed

duality for exotic bialgebras in the classification of hietarinta three triangular 4 4 r matrices lead via the frt formalism to matrix bialgebras which are not deformations of the trivial one in this paper we find the bialgebras which are in duality with these three exotic matrix bialgebras we note that the l t duality of frt is not sufficient for the construction of the bialgebras in duality we find also the quantum planes corresponding to these bialgebras both by the wess zumino r matrix method and by manin s method

accelerating the convergence of series representing the free space periodic green s function a method for improving the convergence of the series representing the doubly periodic free space green s function is presented the method consists of successively applying three different transformations to the green s function spectral representation kummer s transformation is first applied to convert the slowly converging spectral representation into the sum of a rapidly converging series and a slowly converging series the latter series is recognized as the spectral representation of the original periodic source distribution radiating in a medium with an imaginary wavenumber application of the poisson transformation to this series renders it exponentially convergent since it effectively represents propagation of point source contributions through a medium with imaginary wavenumber finally shanks transform is plotted versus the number of terms taken in the series numerical results confirm that an improvement in the convergence rate of the series is achieved for a particular convergence criterion

empirical distribution of good channel codes with nonvanishing error probability this paper studies several properties of channel codes that approach the fundamental limits of a given discrete or gaussian memoryless channel with a nonvanishing probability of error the output distribution induced by an capacity achieving code is shown to be close in a strong sense to the capacity achieving output distribution relying on the concentration of measure isoperimetry property enjoyed by the latter it is shown that regular lipschitz functions of channel outputs can be precisely estimated and turn out to be essentially nonrandom and independent of the actual code it is also shown that the output distribution of a good code and the capacity achieving one cannot be distinguished with exponential reliability the random process produced at the output of the channel is shown to satisfy the asymptotic equipartition property

a new characterization of talagrand s transport entropy inequalities and applications we show that talagrand s transport inequality is equivalent to a restricted logarithmic sobolev inequality this result clarifies the links between these two important functional inequalities as an application we give the first proof of the fact that talagrand s inequality is stable under bounded perturbations

the polya information divergence extensions of sanov s theorem and the conditional limit theorem colt are established for a multicolor polya eggenberger pe urn sampling scheme giving the polya information divergence and a polya extension to the maximum relative entropy maxent method polya maxent includes the standard maxent as well as its variants used in bose einstein fermi dirac and intermediate acharya swamy statistics as special cases in the pe setting standard maxent is in general asymptotically inconsistent

galton watson trees with vanishing martingale limit we show that an infinite galton watson tree conditioned on its martingale limit being smaller than varepsilon agrees up to generation k with a regular mu ary tree where mu is the essential minimum of the offspring distribution and the random variable k is strongly concentrated near an explicit deterministic function growing like a multiple of log 1 varepsilon more precisely we show that if mu ge 2 then with high probability as varepsilon downarrow 0 k takes exactly one or two values this shows in particular that the conditioned trees converge to the regular mu ary tree providing an example of entropic repulsion where the limit has vanishing entropy our proofs are based on recent results on the left tail behaviour of the martingale limit obtained by fleischmann and wachtel 11

improving on the cut set bound via geometric analysis of typical sets we consider the discrete memoryless symmetric primitive relay channel where a source x wants to send information to a destination y with the help of a relay z and the relay can communicate to the destination via an error free digital link of rate r 0 while y and z are conditionally independent and identically distributed given x we develop two new upper bounds on the capacity of this channel that are tighter than existing bounds including the celebrated cut set bound our approach significantly deviates from the standard information theoretic approach for proving upper bounds on the capacity of multi user channels we build on the blowing up lemma to analyze the probabilistic geometric relations between the typical sets of the n letter random variables associated with a reliable code for communicating over this channel these relations translate to new entropy inequalities between the n letter random variables involved as an application of our bounds we study an open question posed by cover 1987 namely what is the minimum rate r 0 needed for the z y link in order for the capacity of the relay channel to be equal to that of the broadcast cut we consider the special case when the x y and x z links are both binary symmetric channels our tighter bounds on the capacity of the relay channel immediately translate to tighter lower bounds for r 0 more interestingly we show that when p to 1 2 r 0 geq 0 1803 even though the broadcast channel becomes completely noisy as p to 1 2 and its capacity and therefore the capacity of the relay channel goes to zero a strictly positive rate r 0 is required for the relay channel capacity to be equal to the broadcast bound existing upper bounds on the capacity of the relay channel and the cut set bound in particular would rather imply r 0 to 0 while achievability schemes require r 0 to 1 we conjecture that r 0 to 1 as p to 1 2

a novel approach for the efficient computation of 1 d and 2 d summations a novel computational method is proposed to evaluate 1 d and 2 d summations and integrals which are relatively difficult to compute numerically the method is based on applying a subspace algorithm to the samples of partial sums and approximating them in terms of complex exponentials for a convergent summation the residue of the exponential term with zero complex pole of this approximation corresponds to the result of the summation since the procedure requires the evaluation of relatively small number of terms the computation time for the evaluation of the summation is reduced significantly in addition by using the proposed method very accurate and convergent results are obtained for the summations which are not even absolutely convergent the efficiency and accuracy of the method are verified by evaluating some challenging 1 d and 2 d summations and integrals

kantorovich duality for general transport costs and applications we introduce a general notion of transport cost that encompasses many costs used in the literature including the classical one and weak transport costs introduced by talagrand and marton in the 90 s and prove a kantorovich type duality theorem as a by product we obtain various applications in different directions we give a short proof of a result by strassen on the existence of a martingale with given marginals we characterize the associated transport entropy inequalities together with the log sobolev inequality restricted to convex concave functions some explicit examples of discrete measures satisfying weak transport entropy inequalities are also given

closed form green s function representations in cylindrically stratified media for method of moments applications closed form green s function cfgf representations for cylindrically stratified media which can be used as the kernel of an electric field integral equation are developed the developed cfgf representations can safely be used in a method of moments solution procedure as they are valid for almost all possible source and field points that lie on the same radial distance from the axis of the cylinder such as the air dielectric and dielectric dielectric interfaces including the axial line rho rho and phi phi which has not been available before in the course of obtaining these expressions the conventional spectral domain green s function representations are rewritten in a different form so that i we can attack the axial line problem and ii the method can handle electrically large cylinders available acceleration techniques that exist in the literature are implemented to perform the summation over the cylindrical eigenmodes efficiently lastly the resulting expressions are transformed to the spatial domain using the discrete complex image method with the help of the generalized pencil of function method where a modified two level approach is used numerical results are presented in the form of mutual coupling between two current modes to assess the accuracy of the final spatial domain cfgf representations

classification of quantum group structures on the group gl 2 all quantum group structures on the group gl 2 are classified in addition to the known quantum groups glqp 2 and glhh 2 there exists one exceptional new quantum group glhq 2

strong data processing inequalities and phi sobolev inequalities for discrete channels the noisiness of a channel can be measured by comparing suitable functionals of the input and output distributions for instance the worst case ratio of output relative entropy to input relative entropy for all possible pairs of input distributions is bounded from above by unity by the data processing theorem however for a fixed reference input distribution this quantity may be strictly smaller than one giving the so called strong data processing inequalities sdpis the same considerations apply to an arbitrary phi divergence this paper presents a systematic study of optimal constants in the sdpis for discrete channels including their variational characterizations upper and lower bounds structural results for channels on product probability spaces and the relationship between the sdpis and the so called phi sobolev inequalities another class of inequalities that can be used to quantify the noisiness of a channel by controlling entropy like functionals of the input distribution by suitable measures of input output correlation several applications to information theory discrete probability and statistical physics are discussed

concentration for coulomb gases and coulomb transport inequalities we study the non asymptotic behavior of coulomb gases in dimension two and more such gases are modeled by an exchangeable boltzmann gibbs measure with a singular two body interaction we obtain concentration of measure inequalities for the empirical distribution of such gases around their equilibrium measure with respect to bounded lipschitz and wasserstein distances this implies macroscopic as well as mesoscopic convergence in such distances in particular we improve the concentration inequalities known for the empirical spectral distribution of ginibre random matrices our approach is remarkably simple and bypasses the use of renormalized energy it crucially relies on new inequalities between probability metrics including coulomb transport inequalities which can be of independent interest our work is inspired by the one of maida and maurel segala itself inspired by large deviations techniques our approach allows to recover extend and simplify previous results by rougerie and serfaty

large deviations and the maximum entropy principle for marked point random fields we establish large deviation principles for the stationary and the individual empirical fields of poisson and certain interacting random fields of marked point particles in d the underlying topologies are induced by a class of not necessarily bounded local functions and thus finer than the usual weak topologies our methods yield further that the limiting behaviour of conditional poisson distributions as well as certain distributions of gibbsian type is governed by the maximum entropy principle we also discuss various applications and examples

a new look at entropy for solving linear inverse problems entropy based methods are widely used for solving inverse problems particularly when the solution is known to be positive here we address linear ill posed and noisy inverse problems of the form z ax n with a general convex constraint x spl isin x where x is a convex set although projective methods are well adapted to this context we study alternative methods which rely highly on some information based criteria our goal is to clarify the role played by entropy in this field and to present a new point of view on entropy using general tools and results coming from convex analysis we present then a new and broad scheme for entropic based inversion of linear noisy inverse problems this scheme was introduced by navaza in 1985 in connection with a physical modeling for crystallographic applications and further studied by dacunha castelle and gamboa 1990 important features of this paper are i a unified presentation of many well known reconstruction criteria ii proposal of new criteria for reconstruction under various prior knowledge and with various noise statistics iii a description of practical inversion of data using the aforementioned criteria and iv a presentation of some reconstruction results

information and entropy econometrics editor s view amos golan department of economics american university roper 200 4400 massachusetts ave nw washington dc 20016 usa

quantum 1 1 extended galilei algebras from lie bialgebras to quantum r matrices and integrable systems the lie bialgebras of the 1 1 extended galilei algebra are obtained and classified into four multiparametric families their quantum deformations are obtained together with the corresponding deformed casimir operators for the coboundary cases quantum universal r matrices are also given applications of the quantum extended galilei algebras to classical integrable systems are explicitly developed

discontinuous condensation transition and nonequivalence of ensembles in a zero range process we study a zero range process where the jump rates do not only depend on the local particle configuration but also on the size of the system rigorous results on the equivalence of ensembles are presented characterizing the occurrence of a condensation transition in contrast to previous results the phase transition is discontinuous and the system exhibits ergodicity breaking and metastable phases this leads to a richer phase diagram including nonequivalence of ensembles in certain phase regions the paper is motivated by results from granular clustering where these features have been observed experimentally

information inequalities and concentration of measure we derive inequalities of the form p q h p r h q r which hold for every choice of probability measures p q r where h p r denotes the relative entropy of p with respect to r and p q stands for a coupling type distance between p and q using the chain rule for relative entropies and then specializing to q with a given support we recover some of talagrand s concentration of measure inequalities for product spaces

classification of real three dimensional poisson lie groups all real three dimensional poisson lie pl groups are explicitly constructed and fully classified under group automorphisms by making use of their one to one correspondence with the complete classification of real three dimensional lie bialgebras given in gomez 2000 j math phys 41 4939 many of these 3d pl groups are non coboundary structures whose poisson brackets are given here for the first time casimir functions for all three dimensional pl groups are given and some features of several pl structures are commented

measure concentration for a class of random processes let x x i i be a stationary random process with a countable alphabet and distribution q let q x k 0 denote the conditional distribution of x x 1 x 2 x n given the k length past write d 1 x 1 0 if 1 x 1 and d 1 x 1 1 otherwise we say that the process x admits a joining with finite distance u if for any two past sequences k 0 k 1 0 and x k 0 x k 1 x 0 there is a joining of q k 0 and q x k 0 say dist 0 x 0 k 0 x k 0 such that the main result of this paper is the following inequality for processes that admit a joining with finite distance

generalized pencil of function method for extracting poles of an em system from its transient response a generalized pencil of function gpof method is developed for extracting the poles of an electromagnetic system from its transient response the gpof method needs the solution of a generalized eigenvalue problem to find the poles subspace decomposition is also used to optimize the performance of the gpof method the gpof method has advantages over the prony method in both computation and noise sensitivity and approaches the cramer rao bound when the signal to noise ratio snr is above threshold an application of the gpof method to a thin wire target is presented

a proof of the strong converse theorem for gaussian multiple access channels we prove the strong converse for the n source gaussian multiple access channel in particular we show that any rate tuple that can be supported by a sequence of codes with asymptotic average error probability 1 must lie in the cover wyner capacity region our proof consists of the following first we perform an expurgation step to convert any given sequence of codes with asymptotic average error probability 1 to codes with asymptotic maximal error probability 1 second we quantize the input alphabets with an appropriately chosen resolution upon quantization we apply the wringing technique by ahlswede on the quantized inputs to obtain further subcodes from the subcodes obtained in the expurgation step so that the resultant correlations among the symbols transmitted by the different sources vanish as the blocklength grows finally we derive upper bounds on achievable sum rates of the subcodes in terms of the type ii error of a binary hypothesis test these upper bounds are then simplified through judicious choices of auxiliary output distributions our strong converse result carries over to the gaussian interference channel under strong interference as long as the sum of the two asymptotic average error probabilities 1

the quantum group glh 2 among all quantum group structures on the space mat 2 of 2 by 2 matrices how many have a central quantum determinant so that one can define quantum sl 2 out of quantum gl 2 up to isomorphism there are two such structures glq 2 and glh 2 the former is well known the latter is described in this letter

comparative analysis of acceleration techniques for 2 d and 3 d green s functions in periodic structures along one and two directions the problem of accelerating the calculation of the periodic green s function is addressed here for both 3 d and 2 d free space configurations in the 3 d case periodicity is considered both along one axis and along two generally skew axes a comprehensive review of the existing methods is first presented and some extensions are developed the possibility of treating the case of complex phase shifts between unit cells necessary for the study of complex modes in periodic structures is also investigated comparisons among the various acceleration methods are performed thus providing fundamental information on their actual efficiency in typical problems

sharp inequalities for f divergences f divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability mathematical statistics and information theory such as kullback leibler divergence chi squared divergence squared hellinger distance total variation distance and so on in this paper we study the problem of maximizing or minimizing an f divergence between two probability measures subject to a finite number of constraints on other f divergences we show that these infinite dimensional optimization problems can all be reduced to optimization problems over small finite dimensional spaces which are tractable our results lead to a comprehensive and unified treatment of the problem of obtaining sharp inequalities between f divergences we demonstrate that many of the existing results on inequalities between f divergences can be obtained as special cases of our results we also improve on some existing non sharp inequalities

characterization of talagrand s like transportation cost inequalities on the real line abstract in this paper we give necessary and sufficient conditions for talagrand s like transportation cost inequalities on the real line this brings a new wide class of examples of probability measures enjoying a dimension free concentration of measure property another byproduct is the characterization of modified log sobolev inequalities for log concave probability measures on r

the heat flow on metric random walk spaces abstract in this paper we study the heat flow on metric random walk spaces which unifies into a broad framework the heat flow on locally finite weighted connected graphs the heat flow determined by finite markov chains and some nonlocal evolution problems we give different characterizations of the ergodicity and prove that a metric random walk space with positive ollivier ricci curvature is ergodic furthermore we prove a cheeger inequality and as a consequence we show that a poincare inequality holds if and only if an isoperimetric inequality holds we also study the bakry emery curvature dimension condition and its relation with functional inequalities like the poincare inequality and the transport information inequalities

statistical inference under multiterminal data compression this paper presents a survey of the literature on the information theoretic problems of statistical inference under multiterminal data compression with rate constraints significant emphasis is put on problems 1 multiterminal hypothesis testing 2 multiterminal parameter estimation and 3 multiterminal pattern classification in either case of positive rates or zero rates in addition the paper includes three new results i e the converse theorems for all problems of multiterminal hypothesis testing multiterminal parameter estimation and multiterminal pattern classification at the zero rate

a simple proof of the blowing up lemma corresp the blowing up lemma says that if the probability with respect to a product measure of a set a subseteq cal x n cal x finite n large is not exponentially small then its l n neighborhood has probability almost one for some l n o n here an information theoretic proof of the blowing up lemma generalizing it to continuous alphabets is given

a new look at independence the concentration of measure phenomenon in product spaces is a farreaching abstract generalization of the classical exponential inequalities for sums of independent random variables we attempt to explain in the simplest possible terms the basic concepts underlying this phenomenon the basic method to prove concentration inequalities and the meaning of several of the most useful inequalities

on combined standard nonstandard or hybrid q h deformations combined q h deformations proposed by kupershmidt and ballesteros herranz parashar are studied in each case a transformation is shown to lead to an equivalent standard q deformation we briefly indicate that appropriate singular limits of the same type of transformations can however lead from standard biparametric p q deformations to nonhybrid but biparametric nonstandard g h ones finally a case of hybrid q h deformation is recalled related to the superalgebra gl 1 1

capacity upper bounds for the relay channel via reverse hypercontractivity we revisit the primitive relay channel introduced by cover in 1987 recent work derived upper bounds on the capacity of this channel that are tighter than the classical cutset bound using the concentration of measure in this paper we recover generalize and improve upon some of these upper bounds with simpler proofs using reverse hypercontractivity to our knowledge this is the first application of reverse hypercontractivity in proving first order converses in network information theory

poincare type inequalities for group measure spaces and related transportation cost inequalities let g be a countable discrete group with an orthogonal representation on a real hilbert space h we prove lp poincare inequalities for the group measure space l h g where both the group action and the gaussian measure space h are associated with the representation the idea of proof comes from pisier s method on the boundedness of riesz transform and lust piquard s work on spin systems then we deduce a transportation type inequality from the lp poincare inequalities in the general noncommutative setting this inequality is sharp up to a constant in the gaussian setting several applications are given including wiener rademacher chaos estimation and new examples of rieffel s compact quantum metric spaces

concentration inequalities using the entropy method we investigate a new methodology worked out by ledoux and massart to prove concentration of measure inequalities the method is based on certain modified logarithmic sobolev inequalities we provide some very simple and general ready to use inequalities one of these inequalities may be considered as an exponential version of the efron stein inequality the main purpose of this paper is to point out the simplicity and the generality of the approach we show how the new method can recover many of talagrand s revolutionary inequalities and provide new applications in a variety of problems including rademacher averages rademacher chaos the number of certain small subgraphs in a random graph and the minimum of the empirical risk in some statistical estimation problems

an on line universal lossy data compression algorithm via continuous codebook refinement i basic results a new on line universal lossy data compression algorithm is presented for finite memoryless sources with unknown statistics its performance asymptotically approaches the fundamental rate distortion limit the codebook is generated on the fly and continuously adapted by simple rules there is no separate codebook training or codebook transmission candidate codewords are randomly generated according to an arbitrary and possibly suboptimal distribution through a carefully designed gold washing or information theoretic sieve mechanism good codewords and only good codewords are promoted to permanent status with high probability we also determine the rate at which our algorithm approaches the fundamental limit

multiple description source coding with no excess marginal rate multiple description source coding concerns situations in which the transmission of the source information is distributed over two data streams at rates r sub 1 and r sub 2 respectively when both data streams are received the decoder uses the combined data at rate r sub 1 r sub 2 to reconstruct the source information with average distortion d sub 0 if a communication breakdown prevents one of the data streams from reaching the receiver the decoder has to base its reconstruction solely on the available data at rate either r sub 1 or r sub 2 this results in a higher distortion of either d sub 1 or d sub 2 respectively the region spl rscr of all achievable quintuples r sub 1 r sub 2 d sub 0 d sub 1 d sub 2 has been determined in the so called no excess rate sum case defined by imposing the requirement r sub 1 r sub 2 r d sub 0 where r spl middot is the rate distortion function of the source the case with excess rate sum characterized by r sub 1 r sub 2 r d sub 0 is challenging we study in this paper a special case of it in which the requirements r sub t r d sub t t 1 2 are imposed we refer to this as the no excess marginal rate case the lower and upper bounds on d sub 0 we obtain are separated by only a tiny gap when evaluated for a binary equiprobable source and the hamming distortion measure

properties of isoperimetric functional and transport entropy inequalities via concentration various properties of isoperimetric functional transport entropy and concentration inequalities are studied on a riemannian manifold equipped with a measure whose generalized ricci curvature is bounded from below first stability of these inequalities with respect to perturbation of the measure is obtained the extent of the perturbation is measured using several different distances between perturbed and original measure such as a one sided l bound on the ratio between their densities wasserstein distances and kullback leibler divergence in particular an extension of the holley stroock perturbation lemma for the log sobolev inequality is obtained and the dependence on the perturbation parameter is improved from linear to logarithmic second the equivalence of transport entropy inequalities with different cost functions is verified by obtaining a reverse jensen type inequality the main tool used is a previous precise result on the equivalence between concentration and isoperimetric inequalities in the described setting of independent interest is a new dimension independent characterization of transport entropy inequalities with respect to the 1 wasserstein distance which does not assume any curvature lower bound

on minimizing distortion and relative entropy a common approach for estimating a probability mass function w when given a prior q and moment constraints given by aw spl les b is to minimize the relative entropy between w and q subject to the set of linear constraints in such cases the solution w is known to have exponential form we consider the case in which the linear constraints are noisy uncertain infeasible or otherwise soft a solution can then be obtained by minimizing both the relative entropy and violation of the constraints aw spl les b a penalty parameter spl sigma weights the relative importance of these two objectives we show that this penalty formulation also yields a solution w with exponential form if the distortion is based on an spl lscr sub p norm then the exponential form of w is shown to have exponential decay parameters that are bounded as a function of spl sigma we also state conditions under which the solution w to the penalty formulation will result in zero distortion so that the moment constraints hold exactly these properties are useful in choosing penalty parameters evaluating the impact of chosen penalty parameters and proving properties about methods that use such penalty formulations

the interactions between ergodic theory and information theory information theorists frequently use the ergodic theorem likewise entropy concepts are often used in information theory recently the two subjects have become partially intertwined as deeper results from each discipline find use in the other a brief history of this interaction is presented in this paper together with a more detailed look at three areas of connection namely recurrence theory blowing up bounds and direct sample path methods

strong converse using change of measure arguments the strong converse for a coding theorem shows that the optimal asymptotic rate possible with vanishing error cannot be improved by allowing a fixed error building on a method introduced by gu and effros for centralized coding problems we develop a general and simple recipe for proving strong converse that is applicable for distributed problems as well heuristically our proof of strong converse mimics the standard steps for proving a weak converse except that we apply those steps to a modified distribution obtained by conditioning the original distribution on the event that no error occurs a key component of our recipe is the replacement of the hard markov constraints implied by the distributed nature of the problem with a soft information cost using a variational formula introduced by oohama we illustrate our method by providing a short proof of the strong converse for the wyner ziv problem and strong converse theorems for interactive function computation common randomness and secret key agreement and the wiretap channel the latter three strong converse problems were open prior to this work

information recovery from pairwise measurements this paper is concerned with jointly recovering n node variables left x i right 1 leq i leq n from a collection of pairwise difference measurements imagine we acquire a few observations taking the form of x i x j the observation pattern is represented by a measurement graph mathcal g with an edge set mathcal e such that x i x j is observed if and only if i j in mathcal e to account for noisy measurements in a general manner we model the data acquisition process by a set of channels with given input output transition measures employing information theoretic tools applied to channel decoding problems we develop a unified framework to characterize the fundamental recovery criterion which accommodates general graph structures alphabet sizes and channel transition measures in particular our results isolate a family of minimum channel divergence measures to characterize the degree of measurement corruption which together with the size of the minimum cut of mathcal g dictates the feasibility of exact information recovery for various homogeneous graphs the recovery condition depends almost only on the edge sparsity of the measurement graph irrespective of other graphical metrics alternatively the minimum sample complexity required for these graphs scales like n log n mathsf hel 1 2 min for certain information metric mathsf hel 1 2 min defined in the main text as long as the alphabet size is not super polynomial in n we apply our general theory to three concrete applications including the stochastic block model the random corruption model and the haplotype assembly problem our theory leads to orderwise tight recovery conditions for all these scenarios

a large deviation approach to some transportation cost inequalities new transportation cost inequalities are derived by means of elementary large deviation reasonings their dual characterization is proved this provides an extension of a well known result of s bobkov and f gotze their tensorization properties are investigated sufficient conditions and necessary conditions too for these inequalities are stated in terms of the integrability of the reference measure applying these results leads to new deviation results concentration of measure and deviations of empirical processes

condensation in stochastic particle systems with stationary product measures we study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities we review previous work on the stationary behaviour and put it in the context of the equivalence of ensembles providing a general characterization of the condensation transition for homogeneous and inhomogeneous systems in the thermodynamic limit this leads to strengthened results on weak convergence for subcritical systems and establishes the equivalence of ensembles for spatially inhomogeneous systems under very general conditions extending previous results which focused on attractive and finite systems we use relative entropy techniques which provide simple proofs making use of general versions of local limit theorems for independent random variables

wasserstein continuity of entropy and outer bounds for interference channels it is shown that under suitable regularity conditions differential entropy is o sqrt n lipschitz as a function of probability distributions on mathbb r n with respect to the quadratic wasserstein distance under similar conditions discrete shannon entropy is shown to be o n lipschitz in distributions over the product space with respect to ornstein s bar d distance wasserstein distance corresponding to the hamming distance these results together with talagrand s and marton s transportation information inequalities allow one to replace the unknown multi user interference with its independent identically distributed approximations as an application a new outer bound for the two user gaussian interference channel is proved which in particular settles the missing corner point problem of costa 1985

saddle point in the minimax converse for channel coding a minimax metaconverse has recently been proposed as a simultaneous generalization of a number of classical results and a tool for the nonasymptotic analysis in this paper it is shown that the order of optimizing the input and output distributions can be interchanged without affecting the bound in the course of the proof a number of auxiliary results of separate interest are obtained in particular it is shown that the optimization problem is convex and can be solved in many cases by the symmetry considerations as a consequence it is demonstrated that in the latter cases the multiletter input distribution in information spectrum verdu han converse bound can be taken to be a memoryless product of single letter ones a tight converse for the binary erasure channel is rederived by computing the optimal nonproduct output distribution for discrete memoryless channels a conjecture of poor and verdu regarding the tightness of the information spectrum bound on the error exponents is resolved in the negative concept of the channel symmetry group is established and relations with the definitions of symmetry by gallager and dobrushin are investigated

the redundancy of source coding with a fidelity criterion 1 known statistics the problem of redundancy of source coding with respect to a fidelity criterion is considered for any fixed rate r 0 and any memoryless source with finite source and reproduction alphabets and a common distribution p the nth order distortion redundancy d sub n r of fixed rate coding is defined as the minimum of the difference between the expected distortion per symbol of any block code with length n and rate r and the distortion rate function d p r of the source p it is demonstrated that for sufficiently large n d sub n r is equal to spl part spl part r d p r ln n 2n o ln n n where spl part spl part r d p r is the partial derivative of d p r evaluated at r and assumed to exist for any fixed distortion level d 0 and any memoryless source p the nth order rate redundancy r sub n d of coding at fixed distortion level d or by using d semifaithful codes is defined as the minimum of the difference between the expected rate per symbol of any d semifaithful code of length n and the rate distortion function r p d of p evaluated at d it is proved that for sufficiently large n r sub n d is upper bounded by ln n n o ln n n and lower bounded by in n 2n o in n n as a by product the lower bound of r sub n d derived in this paper gives a positive answer to a conjecture proposed by yu and speed 1993