On the analogue of the concavity of entropy power in the Brunn-Minkowski theory

Matthieu Fradelizi; Arnaud Marsiglietti

doi:10.1016/j.aam.2014.02.004

On the analogue of the concavity of entropy power in the Brunn-Minkowski theory

Matthieu Fradelizi, Arnaud Marsiglietti

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Abstract

Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured the 1n-concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We investigate this conjecture and study its relationship with geometric inequalities.

Original language	English (US)
Pages (from-to)	1-20
Number of pages	20
Journal	Advances in Applied Mathematics
Volume	57
DOIs	https://doi.org/10.1016/j.aam.2014.02.004
State	Published - Jun 2014
Externally published	Yes

Bibliographical note

Funding Information:
The authors were supported in part by the Agence Nationale de la Recherche , project GeMeCoD ( ANR 2011 BS01 007 01 ).

Keywords

Brunn-Minkowski
Entropy power
Isoperimetric inequality
Parallel set
Parallel volume

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abstract = "Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured the 1n-concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We investigate this conjecture and study its relationship with geometric inequalities.",

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AU - Marsiglietti, Arnaud

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AB - Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured the 1n-concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We investigate this conjecture and study its relationship with geometric inequalities.

KW - Brunn-Minkowski

KW - Entropy power

KW - Isoperimetric inequality

KW - Parallel set

KW - Parallel volume

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On the analogue of the concavity of entropy power in the Brunn-Minkowski theory

Abstract

Bibliographical note

Keywords

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