A spectral condition for spectral gap: fast mixing in high-temperature Ising models

• 成果类型: Article
• 署名作者: Eldan, Ronen; Koehler, Frederic; Zeitouni, Ofer
• 署名单位: Weizmann Institute of Science; Massachusetts Institute of Technology (MIT)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01085-x
• 发表日期: 2022
• 页码: 1035-1051
• 关键词: logarithmic sobolev inequalities

摘要

We prove that Ising models on the hypercube with general quadratic interactions satisfy a Poincare inequality with respect to the natural Dirichlet form corresponding to Glauber dynamics, as soon as the operator norm of the interaction matrix is smaller than 1. The inequality implies a control on the mixing time of the Glauber dynamics. Our techniques rely on a localization procedure which establishes a structural result, stating that Ising measures may be decomposed into a mixture of measures with quadratic potentials of rank one, and provides a framework for proving concentration bounds for high temperature Ising models.