Nonlinear Inequalities and Entropy-Concurrence Plane

Hypergraphs, Entropy, and Inequalities

1. INTRODUCTION. Hypergraphs. Information Theory. Cauchy-Schwarz. It seems reasonable to assume that most mathematicians would be puzzled to find these three terms as, say, key words for the same mathematical paper. (Just in case this puzzlement is a result of being unfamiliar with the term " hypergraph " : a hypergraph is nothing other than a family of sets, and will be defined formally later....

Diffusion equations and entropy inequalities

The present notes contain the material presented at the XLI Summer School on Mathematical Physics (Ravello September 05 10, 2016). The notes aim in introducing a physical way to look at well-known functional inequalities in sharp form. Among them, the classical Young’s inequality and its converse in sharp form, BrascampLieb type inequalities, Babenko’s inequality and Prékopa-Leindler inequality...

Moment - Entropy Inequalities

A note on inequalities for Tsallis relative operator entropy

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...

On Rényi entropy power inequalities

This paper is a follow-up of a recent work by Bobkov and Chistyakov, obtaining some improved Rényi entropy power inequalities (R-EPIs) for sums of independent random vectors. The first improvement relies on the same bounding techniques used in the former work, while the second significant improvement relies on additional interesting properties from matrix theory. The improvements obtained by th...