A Note on the Spectral Gap for Log-Concave Probability Measures on Convex Bodies

Abstract In this paper, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, position of the origin, etc.) on the spectral gap of log-concave probability measures on convex bodies. Our results are illustrated by some classical and less classical examples.

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Publication Details

Journal
International Mathematics Research Notices
Published
2024-11-29
DOI
https://doi.org/10.1093/imrn/rnae256
Primary Topic
Point processes and geometric inequalities
Type
article
Field-Weighted Citation Impact
0.00

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article

A Note on the Spectral Gap for Log-Concave Probability Measures on Convex Bodies

Aldéric Joulin, Michel Bonnefont
International Mathematics Research Notices
Point processes and geometric inequalities
article

A Note on the Spectral Gap for Log-Concave Probability Measures on Convex Bodies

Aldéric Joulin, Michel Bonnefont
article en

Abstract

Abstract In this paper, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, position of the origin, etc.) on the spectral gap of log-concave probability measures on convex bodies. Our results are illustrated by some classical and less classical examples.

International Mathematics Research NoticesVol. 2024(24)
Centre National de la Recherche Scientifique (FR), Université de Bordeaux (FR), Université Fédérale de Toulouse Midi-Pyrénées (FR), Institut de Mathématiques de Bordeaux (FR), Institut de Mathématiques de Toulouse (FR)
Agence Nationale de la Recherche, Centre National de la Recherche Scientifique, Centre International de Mathématiques et Informatique de Toulouse
Reduced inequalities
Openalex Percentile: Top 99%
Point processes and geometric inequalities
DOIOpen Access PDFOpenAlex
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A Note on the Spectral Gap for Log-Concave Probability Measures on Convex Bodies — Aldéric Joulin, Michel Bonnefont · International Mathematics Research Notices (2024) | TGRS Research Map | TGRS