A general two-scale criteria for logarithmic Sobolev inequalities

Tony Lelièvre

doi:10.1016/j.jfa.2008.09.019

A general two-scale criteria for logarithmic Sobolev inequalities

Tony Lelièvre

INRIA Rocquencourt

Research output: Contribution to journal › Article › peer-review

Abstract

We present a general criteria to prove that a probability measure satisfies a logarithmic Sobolev inequality, knowing that some of its marginals and associated conditional laws satisfy a logarithmic Sobolev inequality. This is a generalization of a result by N. Grunewald et al. [N. Grunewald, F. Otto, C. Villani, M.G. Westdickenberg, A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit, Ann. Inst. H. Poincaré Probab. Statist., in press].

Original language	English
Pages (from-to)	2211-2221
Number of pages	11
Journal	Journal of Functional Analysis
Volume	256
Issue number	7
DOIs	https://doi.org/10.1016/j.jfa.2008.09.019
Publication status	Published - 1 Apr 2009

Keywords

Logarithmic Sobolev inequality
Two-scale criteria

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10.1016/j.jfa.2008.09.019

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abstract = "We present a general criteria to prove that a probability measure satisfies a logarithmic Sobolev inequality, knowing that some of its marginals and associated conditional laws satisfy a logarithmic Sobolev inequality. This is a generalization of a result by N. Grunewald et al. [N. Grunewald, F. Otto, C. Villani, M.G. Westdickenberg, A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit, Ann. Inst. H. Poincar{\'e} Probab. Statist., in press].",

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N2 - We present a general criteria to prove that a probability measure satisfies a logarithmic Sobolev inequality, knowing that some of its marginals and associated conditional laws satisfy a logarithmic Sobolev inequality. This is a generalization of a result by N. Grunewald et al. [N. Grunewald, F. Otto, C. Villani, M.G. Westdickenberg, A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit, Ann. Inst. H. Poincaré Probab. Statist., in press].

AB - We present a general criteria to prove that a probability measure satisfies a logarithmic Sobolev inequality, knowing that some of its marginals and associated conditional laws satisfy a logarithmic Sobolev inequality. This is a generalization of a result by N. Grunewald et al. [N. Grunewald, F. Otto, C. Villani, M.G. Westdickenberg, A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit, Ann. Inst. H. Poincaré Probab. Statist., in press].

KW - Logarithmic Sobolev inequality

KW - Two-scale criteria

UR - https://www.scopus.com/pages/publications/60949099340

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DO - 10.1016/j.jfa.2008.09.019

M3 - Article

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SN - 0022-1236

VL - 256

SP - 2211

EP - 2221

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 7

ER -

A general two-scale criteria for logarithmic Sobolev inequalities

Abstract

Keywords

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