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2012 Concavity of entropy along binomial convolutions
Erwan Hillion
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Electron. Commun. Probab. 17: 1-9 (2012). DOI: 10.1214/ECP.v17-1707

Abstract

Motivated by a generalization of Sturm-Lott-Villani theory to discrete spaces and by a conjecture stated by Shepp and Olkin about the entropy of sums of Bernoulli random variables, we prove the concavity in $t$ of the entropy of the convolution of a probability measure $a$, which has the law of a sum of independent Bernoulli variables, by the binomial measure of parameters $n\geq 1$ and $t$.

Citation

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Erwan Hillion. "Concavity of entropy along binomial convolutions." Electron. Commun. Probab. 17 1 - 9, 2012. https://doi.org/10.1214/ECP.v17-1707

Information

Accepted: 6 January 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1246.60031
MathSciNet: MR2872573
Digital Object Identifier: 10.1214/ECP.v17-1707

Subjects:
Primary: 60E15
Secondary: 94A17

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