Formulae for the derivative of the Poincare constant of Gibbs measures

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:140

Article

Sieber, Julian¹ 

[1] Imperial Coll London, Dept Math, London SW7 2AZ, England

关键词: Poincare inequality;    Gibbs measure;    Log-Sobolev inequality;    XY model;   

DOI  :  10.1016/j.spa.2021.06.004

来源: Elsevier

【 摘 要 】

We establish formulae for the derivative of the Poincare constant of Gibbs measures on both compact domains and all of Rd. As an application, we show that if the (not necessarily convex) Hamiltonian is an increasing function, then the Poincare constant is strictly decreasing in the inverse temperature, and vice versa. Applying this result to the O(2) model allows us to give a sharpened upper bound on its Poincare constant. We further show that this model exhibits a qualitatively different zero-temperature behavior of the Poincare and Log-Sobolev constants. (C) 2021 ElsevierB.V. All rights reserved.

【 授权许可】

Free