Related papers: An information-theoretic proof of a hypercontracti…
We revisit and comment on the Harnack type determinantal inequality for contractive matrices obtained by Tung in the nineteen sixtieth and give an extension of the inequality involving multiple positive semidefinite matrices.
A strengthened Lindblad inequality has been proved. We have applied this result for proving a generalized $H$-theorem in non equilibrium thermodynamics. Information processing also can be considered as some thermodynamic process. From this…
We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting…
An inequality is derived for the correlation of two univariate functions operating on symmetric bivariate normal random variables. The inequality is a simple consequence of the Cauchy-Schwarz inequality.
We address the practical problems of estimating the information relations that characterize large networks. Building on methods developed for analysis of the neural code, we show that reliable estimates of mutual information can be obtained…
New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of $n$ independent random variables to the information contained…
New results related to the Boas-Bellman generalisation of Bessel's inequality in inner product spaces are given.
By using quasi-Banach techniques as key ingredient we prove Poincar\'e- and Sobolev- type inequalities for $m$-subharmonic functions with finite $(p,m)$-energy. A consequence of the Sobolev type inequality is a partial confirmation of B\l…
This paper proposes a unifying variational approach for proving and extending some fundamental information theoretic inequalities. Fundamental information theory results such as maximization of differential entropy, minimization of Fisher…
We introduce an information theoretic measure of statistical structure, called 'binding information', for sets of random variables, and compare it with several previously proposed measures including excess entropy, Bialek et al.'s…
We present an elementary proof of a conjecture by I. Ra\c{s}a which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive very recently by the use of stochastic convex orderings. Moreover,…
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.
In \cite{Nam} Nam proved a Lieb--Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a stronger version of this inequality, with…
The Loomis-Whitney inequality, and the more general Uniform Cover inequality, bound the volume of a body in terms of a product of the volumes of lower-dimensional projections of the body. In this paper, we prove stability versions of these…
We give a simple alternative proof of Royen's Gaussian Correlation inequality by using (a slightly generalized version of) Nakamura-Tsuji's symmetric inverse Brascamp-Lieb inequality for even log-concave functions. We explain that this…
Two simple proofs of the triangle inequality for the Jaccard distance in terms of nonnegative, monotone, submodular functions are given and discussed.
In this paper, we provide a concise proof of Oppenheim's double inequality relating to the cosine and sine functions. In passing, we survey this topic.
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.