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Measure comparison problems for dilations of convex bodies

Part of: General convexity Limit theorems Nonlinear functional analysis

Published online by Cambridge University Press:  08 January 2025

Malak Lafi  and
Artem Zvavitch Open the ORCID record for Artem Zvavitch [Opens in a new window]
Malak Lafi
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH, 44242 e-mail: mlafi1@kent.edu
Artem Zvavitch*
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH, 44242 e-mail: mlafi1@kent.edu
*
e-mail: azvavitc@kent.edu
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Abstract

We study a version of the Busemann-Petty problem for $\log $-concave measures with an additional assumption on the dilates of convex, symmetric bodies. One of our main tools is an analog of the classical large deviation principle applied to $\log $-concave measures, depending on the norm of a convex body. We hope this will be of independent interest.

Keywords

Busemann-Petty problemlog-concavitylarge deviation

MSC classification

Primary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces) 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
Secondary: 46T12: Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds 60F10: Large deviations
Type
Article
Information
Canadian Mathematical Bulletin , Volume 68 , Issue 1 , March 2025 , pp. 270 - 285
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

Both authors are supported in part by the U.S. National Science Foundation Grant DMS-1101636 and the United States - Israel Binational Science Foundation (BSF) Grant 2018115.

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