Low-Temperature Asymptotics of the Poincar\'e and the log-Sobolev Constants for {\L}ojasiewicz Potentials

Aziz Ben Nejma

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arXiv · 2604.01785

Low-Temperature Asymptotics of the Poincar\'e and the log-Sobolev Constants for {\L}ojasiewicz Potentials

Aziz Ben Nejma

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Abstract

In this paper, we establish the low-temperature asymptotics of the Poincar\'e inequality constant for a class of convex potentials satisfying a {\L}ojasiewicz inequality. In addition, we disprove a conjecture previously posed by Chewi and Stromme on the low-temperature asymptotics of the log-Sobolev constant and determine the correct asymptotic behavior in dimension one.

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Aziz Ben Nejma. 2026-04-02. Low-Temperature Asymptotics of the Poincar\'e and the log-Sobolev Constants for {\L}ojasiewicz Potentials. https://arxiv.org/abs/2604.01785

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