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Concentration functions and entropy bounds for discrete log-concave distributions

Part of: Communication, information Distribution theory - Probability

Published online by Cambridge University Press:  27 May 2021

Sergey G. Bobkov ,
Arnaud Marsiglietti  and
James Melbourne
Sergey G. Bobkov
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN55455, USA
Arnaud Marsiglietti*
Affiliation:
University of Florida, Department of Mathematics, Gainesville, FL32611, USA
James Melbourne
Affiliation:
Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN55455, USA
*
*Corresponding author. Email: a.marsiglietti@ufl.edu
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Abstract

Two-sided bounds are explored for concentration functions and Rényi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 94A17: Measures of information, entropy 39B62: Functional inequalities, including subadditivity, convexity, etc.
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 31 , Issue 1 , January 2022 , pp. 54 - 72
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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