Entropy and thinning of discrete random variables

Oliver T Johnson

doi:10.1007/978-1-4939-7005-6_2

Entropy and thinning of discrete random variables

Oliver T Johnson

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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 language	English
Title of host publication	Convexity and concentration
Subtitle of host publication	proceedings of the Spring 2015 Semester of the Theme Year in Discrete Structures, IMA Minneapolis
Editors	Eric Carlen, Mokshay Madiman, Elisabeth Werner
Publisher	Springer
Pages	33-53
ISBN (Electronic)	9781493970056
ISBN (Print)	9781493970049
DOIs	https://doi.org/10.1007/978-1-4939-7005-6_2
Publication status	Published - 21 Apr 2017

Publication series

Name	The IMA Volumes in Mathematics and its Applications
Publisher	Springer
Volume	161
ISSN (Print)	0940-6573

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10.1007/978-1-4939-7005-6_2

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http://arxiv.org/abs/1510.05390

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Johnson, O. T. (2017). Entropy and thinning of discrete random variables. In E. Carlen, M. Madiman, & E. Werner (Eds.), Convexity and concentration: proceedings of the Spring 2015 Semester of the Theme Year in Discrete Structures, IMA Minneapolis (pp. 33-53). (The IMA Volumes in Mathematics and its Applications; Vol. 161). Springer. https://doi.org/10.1007/978-1-4939-7005-6_2

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Entropy and thinning of discrete random variables. / Johnson, Oliver T.
Convexity and concentration: proceedings of the Spring 2015 Semester of the Theme Year in Discrete Structures, IMA Minneapolis. ed. / Eric Carlen; Mokshay Madiman; Elisabeth Werner. Springer, 2017. p. 33-53 (The IMA Volumes in Mathematics and its Applications; Vol. 161).

Research output: Chapter in Book/Report/Conference proceeding › Chapter in a book

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N2 - 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.

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A2 - Madiman, Mokshay

A2 - Werner, Elisabeth

PB - Springer

ER -

Entropy and thinning of discrete random variables

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