delay independence of mutual information rate of two symbolic sequences introduced by shannon as a rate of actual transmission mutual information rate mir is an extension of mutual information to a pair of dynamical processes we show a delay independence theorem according to which mir is not sensitive to a time shift between the two processes numerical studies of several benchmark situations confirm that this theoretical asymptotic property remains valid for realistic finite sequences estimations based on block entropies and a causal state machine algorithm perform better than an estimation based on a lempel ziv compression algorithm provided that block length and maximum history length respectively can be chosen larger than the delay mir is thus a relevant index for measuring nonlinear correlations between two experimental or simulated sequences when the transmission delay in input output devices or dephasing in coupled systems is variable or unknown

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

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

concentration of quantum states from quantum functional and transportation cost inequalities quantum functional inequalities e g the logarithmic sobolev and poincare inequalities have found widespread application in the study of the behavior of primitive quantum markov semigroups the classical counterparts of these inequalities are related to each other via a so called transportation cost inequality of order 2 tc2 the latter inequality relies on the notion of a metric on the set of probability distributions called the wasserstein distance of order 2 tc2 in turn implies a transportation cost inequality of order 1 tc1 in this paper we introduce quantum generalizations of the inequalities tc1 and tc2 making use of appropriate quantum versions of the wasserstein distances one recently defined by carlen and maas and the other defined by us we establish that these inequalities are related to each other and to the quantum modified logarithmic sobolev and poincare inequalities as in the classical case we also show that these inequalities imply certain concentration type results

existence of infinitely many solutions for a neumann problem involving the p x laplacian abstract in this paper we consider the neumann problem involving the p x laplacian of the type div u p x 2 u x u p x 2 u f x u g x u in u 0 on we prove the existence of infinitely many solutions of the problem under weaker hypotheses by applying a variational principle due to b ricceri and the theory of the variable exponent sobolev spaces our results are an improvement and generalization of the relative results obtained by b ricceri for the p laplacian case

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

duality theorems for joint source channel coding we consider joint source channel coding for a memoryless gaussian source and an additive white gaussian noise awgn channel for a given code defined by an encoder decoder pair spl alpha spl beta its dual code is obtained by interchanging the encoder and decoder spl beta spl alpha it is shown that if a code spl alpha spl beta is optimal at rate p channel uses per source sample and if it satisfies a certain uniform continuity condition then its dual code spl beta spl alpha is optimal for rate 1 spl rho channel uses per source sample further it is demonstrated that there is a code which is optimal but its dual code is not optimal finally using random coding we show that there is an optimal code which has an optimal dual the duality concept is also presented for the cases of i binary memoryless equiprobable source and binary symmetric channel bsc and ii colored gaussian source and additive colored gaussian noise acgn channel

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

a multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids the goal of this correction is to correct a mistake that appears in the proof of both lemma 3 9 and 3 10 in the article mih ilescu r dulescu 2006 1 the mistake in the proof of lemma 3 9 and 3 10 is mainly owing to the fact that we wrongly computed the expression of function g x t

existence and multiplicity results for boundary value problems connected with the discrete p ź laplacian on weighted finite graphs we use the direct variational method the ekeland variational principle the mountain pass geometry and karush kuhn tucker theorem in order to investigate existence and multiplicity results for boundary value problems connected with the discrete p laplacian on weighted finite graphs several auxiliary inequalities for the discrete p laplacian on finite graphs are also derived positive solutions are considered

existence and multiplicity results for a new p x kirchhoff problem abstract in this work we study the existence and multiplicity results for the following nonlocal p x kirchhoff problem 0 1 a b 1 p x u p x d x d i v u p x 2 u u p x 2 u g x u in u 0 on where a b 0 are constants r n is a bounded smooth domain p c with n p x 1 is a real parameter and g is a continuous function the analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties

singular solutions of the p laplace equation soit un sous ensemble ouvert de r n n 1 et p un nombre reel plus grand que 1 on suppose que 0 o et u est p harmonique dans on etudie le comportement de la solution faible u pres de o de l equation apu div u p 2 u 0

on superlinear p x laplacian equations in rn abstract we consider the p x laplacian equations in r n the nonlinearity is superlinear but does not satisfy the ambrosetti rabinowitz type condition we obtain ground states of the equations improving a recent result of fan x l fan p x laplacian equations in r n with periodic data and nonperiodic perturbations j math anal appl 341 2008 103 119 we also establish a bartsch wang type compact embedding theorem for variable exponent spaces then a multiplicity result for the equations is proved for odd nonlinearity

eigenvalues of the p x laplacian steklov problem abstract consider steklov eigenvalue problem involving the p x laplacian on a bounded domain the open subset of r n with n 2 as follows p x u u p x 2 u in u p x 2 u u p x 2 u on where p x constant we prove that the existence of infinitely many eigenvalue sequences unlike the p laplacian case for a variable exponent p x constant there does not exist a principal eigenvalue and the set of all eigenvalues is not closed under some assumptions finally we present some sufficient conditions for the infimum of all eigenvalues is zero and positive respectively

exponential inequalities for dynamical measures of expanding maps of the interval we prove an exponential inequality for the absolutely continuous invariant measure of a piecewise expanding map of the interval as an immediate corollary we obtain a concentration inequality we apply these results to the estimation of the rate of convergence of the empirical measure in various metrics and also to the efficiency of the shadowing by sets of positive measure

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

the capacity of the relay channel solution to cover s problem in the gaussian case consider a memoryless relay channel where the relay is connected to the destination with an isolated bit pipe of capacity c 0 let c c 0 denote the capacity of this channel as a function of c 0 what is the critical value of c 0 such that c c 0 first equals c infty this is a long standing open problem posed by cover and named the capacity of the relay channel in open problems in communication and computation springer verlag 1987 in this paper we answer this question in the gaussian case and show that c c 0 cannot equal to c infty unless c 0 infty regardless of the snr of the gaussian channels this result follows as a corollary to a new upper bound we develop on the capacity of this channel instead of single letterizing expressions involving information measures in a high dimensional space as is typically done in converse results in information theory our proof directly quantifies the tension between the pertinent n letter forms this is done by translating the information tension problem to a problem in high dimensional geometry as an intermediate result we develop an extension of the classical isoperimetric inequality on a high dimensional sphere which can be of interest in its own right

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

bounding bar d distance by informational divergence a method to prove measure concentration there is a simple inequality by pinsker between variational distance and informational divergence of probability measures defined on arbitrary probability spaces we shall consider probability measures on sequences taken from countable alphabets and derive from pinsker s inequality bounds on the bar d distance by informational divergence such bounds can be used to prove the concentration of measure phenomenon for some nonproduct distributions

remarks on ricceri s variational principle and applications to the p x laplacian equations abstract in this paper we give some remarks on a variational principle of ricceri in the case of sequentially weakly lower semi continuous functionals defined on a reflexive real banach space in particular we introduce the notions of ricceri block and ricceri box which are more convenient in some applications than the weakly connected components using the variational principle of ricceri and a local mountain pass lemma we study the multiplicity of solutions of the p x laplacian equations with neumann dirichlet or no flux boundary condition and under appropriate hypotheses in which the integral functionals need not satisfy the ps condition on the global space we prove that the problem has at least seven solutions

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

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 multidimensional diffusions and their boundary local times we prove that probability laws of certain multidimensional semimartingales which includes time inhomogenous diffusions under suitable assumptions satisfy quadratic transportation cost inequality under the uniform metric from this we derive concentration properties of lipschitz functions of process paths that depend on the entire history in particular we estimate concentration of boundary local time of reflected brownian motions on a polyhedral domain we work out explicit applications of consequences of measure concentration for the case of brownian motion with rank based drifts

periodic and neumann problems for discrete p laplacian abstract using critical point theory we obtain the existence of solutions for some periodic boundary value problems involving the discrete p laplacian these extend and improve known results for similar problems with discrete p laplacian similar results for neumann problems are also provided as applications we prove upper and lower solutions theorems for both considered cases

positive solutions for discrete boundary value problems involving the p laplacian with potential terms in this paper we discuss the existence and the uniqueness of discrete boundary value problems involving the p laplacian with potential terms to this end we deal with the strong comparison principle and the dirichlet principle for the p laplacian with potential terms on weighted graphs with boundary moreover we provide a lower bound of the potential terms which guarantees the existence of solutions of the boundary value problem for the operator finally we also discuss inverse conductivity and potential problems for the operator

forchheimer law derived by homogenization of gas flow in turbomachines a general formulation of the homogenization problem of compressible fluid flow through a periodic porous material in turbomachines is presented here this formulation is able to derive a forchheimer law with a mean velocity dependent permeability as equivalent macroscopic behavior to specify this permeability additional flow problems are defined on the unit cell and solved by a mixed stabilized finite element discretization the application of the galerkin least square gls method requires the introduction of two stabilization terms with appropriate parameters the mixed finite element discretization of these unit cell problems is finally outlined

on the recovery of joint distributions from limited information the paper considers the role of entropy and other information theoretic concepts in the description and formation of joint distributions for m random variables the discussion includes a review of methods for constructing discrete and continuous joint distributions from the component marginal distributions we then propose a minimum cross entropy approach that recovers continuous joint distributions from the joint and marginal moments and the marginal densities the large sample properties of the associated estimator are outlined and a simple demonstration problem that highlights the advantages and drawbacks of the proposed method is presented

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

concentration inequalities for dependent random variables via the martingale method the martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space with the constants in the inequalities expressed in terms of certain mixing coefficients along the way bounds are obtained on martingale differences associated with the random sequences which may be of independent interest as applications of the main result concentration inequalities are also derived for inhomogeneous markov chains and hidden markov chains and an extremal property associated with their martingale difference bounds is established this work complements and generalizes certain concentration inequalities obtained by marton and samson while also providing different proofs of some known results

existence of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

mountain pass and ekeland s principle for eigenvalue problem with variable exponent in this article we study the boundary value problem div u p x 2 u u x 2 u u q x 2 u in u 0 on where is a smooth bounded domain in n and p q are continuous functions on we show that for any 0 there exists infinitely many weak solutions respectively if 0 and small enough then there exists a non negative non trivial weak solution our approach relies on the variable exponent theory of generalized lebesgue sobolev spaces combined with a 2 symmetric version for even functionals of the mountain pass theorem respectively on simple variational arguments based on ekeland s variational principle this article is devoted to the special issue vaxjo conference 2008

ricci curvature of markov chains on metric spaces abstract we define the coarse ricci curvature of metric spaces in terms of how much small balls are closer in wasserstein transportation distance than their centers are this definition naturally extends to any markov chain on a metric space for a riemannian manifold this gives back after scaling the value of ricci curvature of a tangent vector examples of positively curved spaces for this definition include the discrete cube and discrete versions of the ornstein uhlenbeck process moreover this generalization is consistent with the bakry emery ricci curvature for brownian motion with a drift on a riemannian manifold positive ricci curvature is shown to imply a spectral gap a levy gromov like gaussian concentration theorem and a kind of modified logarithmic sobolev inequality the bounds obtained are sharp in a variety of examples

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

on the discrete boundary value problem for anisotropic equation abstract in this paper we consider the discrete anisotropic boundary value problem using critical point theory firstly we apply the direct method of the calculus of variations and the mountain pass technique in order to reach the existence of at least one nontrivial solution secondly we derive some version of a discrete three critical point theorem which we apply in order to get the existence of at least two nontrivial solutions

randomized quantization and source coding with constrained output distribution this paper studies fixed rate randomized vector quantization under the constraint that the quantizer s output has a given fixed probability distribution a general representation of randomized quantizers that includes the common models in the literature is introduced via appropriate mixtures of joint probability measures on the product of the source and reproduction alphabets using this representation and results from optimal transport theory the existence of an optimal minimum distortion randomized quantizer having a given output distribution is shown under various conditions for sources with densities and the mean square distortion measure it is shown that this optimum can be attained by randomizing quantizers having convex codecells for stationary and memoryless source and output distributions a rate distortion theorem is proved providing a single letter expression for the optimum distortion in the limit of large blocklengths

confounder detection in high dimensional linear models using first moments of spectral measures in this letter we study the confounder detection problem in the linear model where the target variable y is predicted using its n potential causes xn x1 xn t based on an assumption of a rotat

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

on concentration inequalities and their applications for gibbs measures in lattice systems we consider gibbs measures on the configuration space s mathbb z d where mostly d ge 2 and s is a finite set we start by a short review on concentration inequalities for gibbs measures in the dobrushin uniqueness regime we have a gaussian concentration bound whereas in the ising model and related models at sufficiently low temperature we control all moments and have a stretched exponential concentration bound we then give several applications of these inequalities whereby we obtain various new results amongst these applications we get bounds on the speed of convergence of the empirical measure in the sense of kantorovich distance fluctuation bounds in the shannon mcmillan breiman theorem fluctuation bounds for the first occurrence of a pattern as well as almost sure central limit theorems

existence of periodic solutions for p t laplacian systems abstract in this paper by using minimax methods in critical point theory we obtain some existence theorems for periodic solutions of p t laplacian system u t p t 2 u t f t u t 0 u 0 u t u 0 u t 0 and our results generalize some existed theorems

hitting times functional inequalities lyapunov conditions and uniform ergodicity the use of lyapunov conditions for proving functional inequalities was initiated in 5 it was shown in 4 30 that there is an equivalence between a poincare inequality the existence of some lyapunov function and the exponential integrability of hitting times in the present paper we close the scheme of the interplay between lyapunov conditions and functional inequalities by showing that strong functional inequalities are equivalent to lyapunov type conditions showing that these lyapunov conditions are characterized by the finiteness of generalized exponential moments of hitting times we also give some complement concerning the link between lyapunov conditions and in tegrability property of the invariant probability measure and as such transportation inequalities and we show that some unbounded lyapunov conditions can lead to uniform ergodicity and coming down from infinity property

a distribution dependent refinement of pinsker s inequality given two probability distributions q and p let spl par q p spl par sub 1 and d q spl par p respectively denote the l sub 1 distance and divergence between q and p we derive a refinement of pinsker s inequality of the form d q spl par p spl ges c p spl par q p spl par sub 1 sup 2 and characterize the best p dependent factor c p we apply the refined inequality to large deviations and measure concentration

monge kantorovitch measure transportation and monge ampere equation on wiener space let w h be an abstract wiener space assume two i i 1 2 probabilities on w w we give some conditions for the wasserstein distance between 1 and 2 with respect to the cameron martin space to be finite where the infimum is taken on the set of probability measures on w w whose first and second marginals are 1 and 2 in this case we prove the existence of a unique cyclically monotone map t iw with w h such that t maps 1 to 2 moreover if 2 then t is stochastically invertible i e there exists s w w such that s t iw 1 a s and t s iw 2 a s if in addition 1 then there exists a 1 convex function in the gaussian sobolev space such that these results imply that the quasi invariant transformations of the wiener space with finite wasserstein distance from can be written as the composition of a transport map t and a rotation i e a measure preserving map we give also 1 convex sub solutions and ito type solutions of the monge ampere equation on w

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

overview of differential equations with non standard growth abstract differential equations with non standard growth have been a very active field of investigation in recent years in this survey we present an overview of the field as well as several of the most important results we consider both existence and regularity questions finally we provide a comprehensive list of papers published to date

homogenization of the fluid flow and heat transfer in transpiration cooled multi layer plates to predict the aerothermal behavior of transpiration cooled plates a multi scale approach based on the homogenization method of periodic material structures is developed this method allows one to calculate effective equivalent thermophysical properties either for each layer or for the multi layer of superalloy bondcoat and tbc a general formulation is developed here for the fluid flow through a porous media which is able to deduce as equivalent macroscopic behavior either a darcy law with a constant permeability or a more general fochheimer law with a permeability function of the mean velocity effective darcy permeabilities are calculated by solving special stokes flow problems on a unit cell finally effective conductivities and permeabilities are determined for different configurations of cylindrical and shaped transpiration cooling channels

on a dirichlet problem with p x laplacian abstract we show the existence and stability of solutions for a family of dirichlet problems div v z 1 x u v z n x u l u x u f u k x u u w 0 1 p x in a bounded domain and with nonconvex nonlinearity satisfying some local growth conditions the conditions upon v and l allow for considering the p x laplacian equation we use the relations between critical points and critical values to the primal and a suitable dual action functional to get the existence stability and some properties of the solutions

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

a high dimensional clt in mathcal w _2 w 2 distance with near optimal convergence rate let x 1 ldots x n be i i d random vectors in mathbb r d with vert x 1 vert le beta then we show that begin aligned frac 1 sqrt n left x 1 cdots x n right end aligned converges to a gaussian in quadratic transportation also known as kantorovich or wasserstein distance at a rate of o left frac sqrt d beta log n sqrt n right improving a result of valiant and valiant the main feature of our theorem is that the rate of convergence is within log n of optimal for n d rightarrow infty

modified logarithmic sobolev inequalities and transportation inequalities we present a class of modified logarithmic sobolev inequality interpolating between poincare and logarithmic sobolev inequalities suitable for measures of the type exp x or exp x log 2 x 1 2 and which lead to new concentration inequalities these modified inequalities share common properties with usual logarithmic sobolev inequalities as tensorisation or perturbation and imply as well poincare inequality we also study the link between these new modified logarithmic sobolev inequalities and transportation inequalities

rate constrained simulation and source coding i i d sources necessary conditions for asymptotically optimal sliding block or stationary codes for source coding and rate constrained simulation of memoryless sources are presented and used to motivate a design technique for trellis encoded source coding and rate constrained simulation the code structure has intuitive similarities to classic random coding arguments as well as to fake process methods and alphabet constrained methods experimental evidence shows that the approach provides comparable or superior performance in comparison with previously published methods on common examples sometimes by significant margins

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

on a resonance problem with the discrete p laplacian on finite graphs abstract in this paper we discuss the existence of a solution for a resonance problem involving the discrete p laplacian using asymptotic behaviors of g at infinity a nontrivial solution is established moreover we also find a necessary condition for asymptotic behavior of g at zero to guarantee the existence of at least two nontrivial solutions

electro osmotic flows through topographically complicated porous media role of electropermeability tensor in the present work we consider a framework for characterizing electro osmotic flows in topographically complicated porous media and derive an effective up scaled transport parameter to quantify this we term this parameter the electro permeability which characterizes the electro osmotic flow through composite porous media in analogy with darcy s law the electro permeability tensor thus introduced serves a simple means of relating the volume flow rate with the applied electric field without going into the intricacies of the microstructure of the porous domain first we consider cases where the solid fractions have a fractal dimension generated by the mandelbrot set purely for the sake of demonstration based on such considerations we employ the method of homogenization to obtain the effective electro permeability parameter from the numerical simulations executed over a representative volume element our derived electro permeability tensor components exhibit functional relationships with the solid or liquid fraction as well as the topography of the porous medium having established these functional relationships we evaluate the tensor components for a binary composite porous medium in which one constituent has markedly high ensuremath zeta potential than the other constituent for illustration with potential relevance in microfluidics we establish the sensitivity of the electro permeability tensor on the domain morphology solid fraction ratio of solid fractions of the two phases having the two different ensuremath zeta potential values and the ensuremath zeta potential contrast and compare it with equivalent darcy permeability for the same we thus provide a simple mathematical framework that may be immensely helpful for devising a computationally efficient way of characterizing electro osmosis through topographically complicated porous media

on a mixture of brenier and strassen theorems we give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in 33 optimal plans are composition of a deterministic transport given by the gradient of a continuously differentiable convex function followed by a martingale coupling we also establish some connections with caffarelli s contraction theorem 14

transportation information inequalities for markov processes in this paper one investigates the transportation information tci inequalities tc i for all probability measures on a metric space mathcal x d where is a given probability measure tc is the transportation cost from to with respect to the cost function c x y on mathcal x 2 i is the fisher donsker varadhan information of with respect to and 0 0 is a left continuous increasing function using large deviation techniques it is shown that tci is equivalent to some concentration inequality for the occupation measure of a reversible ergodic markov process related to i the tensorization property of tci and comparisons of tci with poincare and log sobolev inequalities are investigated several easy to check sufficient conditions are provided for special important cases of tci and several examples are worked out

minimum kl divergence on complements of l_ 1 balls pinsker s widely used inequality upper bounds the total variation distance left vert p q right vert 1 in terms of the kullback leibler divergence d p vert q although in general a bound in the reverse direction is impossible in many applications the quantity of interest is actually d ast v q defined for an arbitrary fixed q as the infimum of d p vert q over all distributions p that are at least v far away from q in total variation we show that d ast v q leq c v 2 o v 3 where c c q 1 2 for balanced distributions thereby providing a kind of reverse pinsker inequality some of the structural results obtained in the course of the proof may be of independent interest an application to large deviations is given

multiple solutions for neumann and periodic problems with singular ϕ laplacian abstract we use the critical point theory for convex lower semicontinuous perturbations of c 1 functionals to establish existence of multiple radial solutions for some one parameter neumann problems involving the operator v div v 1 v 2 similar results for periodic problems are also provided