Related papers: Concentration functions and entropy bounds for dis…
New class of reference distribution functions for numerical approximation of the solution of the Fokker-Planck equations associated to the charged particle dynamics in tokamak are studied. The reference distribution functions are obtained…
We derive properties of powers of a function satisfying a second-order linear differential equation. In particular we prove that the n-th power of the function satisfies an (n+1)-th order differential equation and give a simple method for…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
Entanglement criteria for an $n$-partite quantum system with continuous variables are formulated in terms of R\'{e}nyi entropies. R\'{e}nyi entropies are widely used as a good information measure due to many nice properties. Derived…
We prove a log-Sobolev inequality for a certain class of log-concave measures in high dimension. These are the probability measures supported on the unit cube in R^n whose density takes the form exp(-H) where the function H is assumed to be…
We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an…
We derive sharp lower bounds for L^p-functions on the n-dimensional unit hypercube in terms of their p-th marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…
We derive two upper bounds for the probability of deviation of a vector-valued Lipschitz function of a collection of random variables from its expected value. The resulting upper bounds can be tighter than bounds obtained by a direct…
When more than one hadron takes part in a hard process, an extended set of quark distribution and fragmentation functions becomes relevant. In this talk, the derivation of Soffer-like bounds for these functions, in the case of a spin-1/2…
The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be…
Starting from the geometrical interpretation of the R\'enyi entropy, we introduce further extensive generalizations and study their properties. In particular, we found the probability distribution function obtained by the MaxEnt principle…
Mixed $f$-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are…
We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincare inequalities for such functions. This leads naturally to the concept of…
We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal…
We obtain bounds on fluctuations of two entropy estimators for a class of one-dimensional Gibbs measures on the full shift. They are the consequence of a general exponential inequality for Lipschitz functions of n variables. The first…
We prove bounds for the covering numbers of classes of convex functions and convex sets in Euclidean space. Previous results require the underlying convex functions or sets to be uniformly bounded. We relax this assumption and replace it…
The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the…