Low-Temperature Asymptotics of the Poincar\'e and the log-Sobolev Constants for ojasiewicz Potentials
Abstract
In this paper, we establish the low-temperature asymptotics of the Poincar\'e inequality constant for a class of convex potentials satisfying a 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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