Entropic Isoperimetric Inequalities

Sergey G. Bobkov; Cyril Roberto

doi:10.1007/978-3-031-26979-0_3

Entropic Isoperimetric Inequalities

Sergey G. Bobkov, Cyril Roberto

School of Mathematics

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

Abstract

We discuss optimal bounds on the Rényi entropies in terms of the Fisher information. In Information Theory, such relations are also known as entropic isoperimetric inequalities.

Original language	English (US)
Title of host publication	Progress in Probability
Publisher	Birkhauser
Pages	97-121
Number of pages	25
DOIs	https://doi.org/10.1007/978-3-031-26979-0_3
State	Published - 2023

Publication series

Name	Progress in Probability
Volume	80
ISSN (Print)	1050-6977
ISSN (Electronic)	2297-0428

Bibliographical note

Funding Information:
Acknowledgments Research of the first author was partially supported by the NSF grant DMS-2154001. Research of the second author was partially supported by the grants ANR-15-CE40-0020-03 – LSD – Large Stochastic Dynamics, ANR 11-LBX-0023-01 – Labex MME-DII and Fondation Simone et Cino del Luca in France. This research has been conducted within the FP2M federation (CNRS FR 2036).

Funding Information:
Research of the first author was partially supported by the NSF grant DMS-2154001. Research of the second author was partially supported by the grants ANR-15-CE40-0020-03 – LSD – Large Stochastic Dynamics, ANR 11-LBX-0023-01 – Labex MME-DII and Fondation Simone et Cino del Luca in France. This research has been conducted within the FP2M federation (CNRS FR 2036).

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Fisher information
Isoperimetric inequality
Rényi entropy

Publisher link

10.1007/978-3-031-26979-0_3

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abstract = "We discuss optimal bounds on the R{\'e}nyi entropies in terms of the Fisher information. In Information Theory, such relations are also known as entropic isoperimetric inequalities.",

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author = "Bobkov, {Sergey G.} and Cyril Roberto",

note = "Funding Information: Acknowledgments Research of the first author was partially supported by the NSF grant DMS-2154001. Research of the second author was partially supported by the grants ANR-15-CE40-0020-03 – LSD – Large Stochastic Dynamics, ANR 11-LBX-0023-01 – Labex MME-DII and Fondation Simone et Cino del Luca in France. This research has been conducted within the FP2M federation (CNRS FR 2036). Funding Information: Research of the first author was partially supported by the NSF grant DMS-2154001. Research of the second author was partially supported by the grants ANR-15-CE40-0020-03 – LSD – Large Stochastic Dynamics, ANR 11-LBX-0023-01 – Labex MME-DII and Fondation Simone et Cino del Luca in France. This research has been conducted within the FP2M federation (CNRS FR 2036). Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2023",

doi = "10.1007/978-3-031-26979-0_3",

language = "English (US)",

series = "Progress in Probability",

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AU - Bobkov, Sergey G.

AU - Roberto, Cyril

N1 - Funding Information: Acknowledgments Research of the first author was partially supported by the NSF grant DMS-2154001. Research of the second author was partially supported by the grants ANR-15-CE40-0020-03 – LSD – Large Stochastic Dynamics, ANR 11-LBX-0023-01 – Labex MME-DII and Fondation Simone et Cino del Luca in France. This research has been conducted within the FP2M federation (CNRS FR 2036). Funding Information: Research of the first author was partially supported by the NSF grant DMS-2154001. Research of the second author was partially supported by the grants ANR-15-CE40-0020-03 – LSD – Large Stochastic Dynamics, ANR 11-LBX-0023-01 – Labex MME-DII and Fondation Simone et Cino del Luca in France. This research has been conducted within the FP2M federation (CNRS FR 2036). Publisher Copyright: © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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KW - Fisher information

KW - Isoperimetric inequality

KW - Rényi entropy

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SP - 97

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BT - Progress in Probability

PB - Birkhauser

ER -

Entropic Isoperimetric Inequalities

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