Entropy and thinning of discrete random variables

Abstract

We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information theoretic approaches to Poisson approximation, the maximum entropy property of the Poisson distribution, discrete concentration (Poincaré and logarithmic Sobolev) inequalities, monotonicity of entropy and concavity of entropy in the Shepp--Olkin regime.

Draft for Proceedings of IMA theme year in Discrete Structures

References in corpus (4)

• Forward and Reverse Entropy Power Inequalities in Convex Geometry
• A discrete log-Sobolev inequality under a Bakry-Emery type condition
• A proof of the Shepp-Olkin entropy concavity conjecture
• Concavity of entropy under thinning