Entropy and thinning of discrete random variables

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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.
Original languageEnglish
Title of host publicationConvexity and concentration
Subtitle of host publicationproceedings of the Spring 2015 Semester of the Theme Year in Discrete Structures, IMA Minneapolis
EditorsEric Carlen, Mokshay Madiman, Elisabeth Werner
PublisherSpringer
Pages33-53
ISBN (Electronic)9781493970056
ISBN (Print)9781493970049
DOIs
Publication statusPublished - 21 Apr 2017

Publication series

NameThe IMA Volumes in Mathematics and its Applications
PublisherSpringer
Volume161
ISSN (Print)0940-6573

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