Logarithmic Sobolev Inequalities

Sergey Bobkov; Gennadiy Chistyakov; Friedrich Götze

doi:10.1007/978-3-031-31149-9_7

Logarithmic Sobolev Inequalities

Sergey Bobkov, Gennadiy Chistyakov, Friedrich Götze

School of Mathematics

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

Abstract

Logarithmic Sobolev inequalities strengthen Poincaré-type inequalities, which allows one to derive sharper deviation inequalities for various classes of functions, not necessarily under the Lipschitz hypothesis. To introduce this class of analytic inequalities, first we briefly mention basic properties of the involved entropy functional and then describe several important examples of measures satisfying logarithmic Sobolev inequalities. The remaining part of the chapter deals with various bounds that are valid in the presence of logarithmic Sobolev inequalities.

Original language	English (US)
Title of host publication	Probability Theory and Stochastic Modelling
Publisher	Springer Nature
Pages	131-147
Number of pages	17
DOIs	https://doi.org/10.1007/978-3-031-31149-9_7
State	Published - 2023

Publication series

Name	Probability Theory and Stochastic Modelling
Volume	104
ISSN (Print)	2199-3130
ISSN (Electronic)	2199-3149

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

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10.1007/978-3-031-31149-9_7

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ER -

Logarithmic Sobolev Inequalities

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