Kawasaki dynamics beyond the uniqueness threshold

• 成果类型: Article
• 署名作者: Bauerschmidt, Roland; Bodineau, Thierry; Dagallier, Benoit
• 署名单位: New York University; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01326-9
• 发表日期: 2025
• 页码: 267-302
• 关键词: logarithmic sobolev inequality; glauber dynamics; spectral gap; ising-models; trees; PROOF

摘要

Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random d-regular graph mixes fast beyond the tree uniqueness threshold when d is large enough (and conjecture that it mixes fast up to the tree reconstruction threshold for all d >= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\geqslant 3$$\end{document}). This result follows from a more general spectral condition for (modified) log-Sobolev inequalities for conservative dynamics of Ising models. The proof of this condition in fact extends to perturbations of distributions with log-concave generating polynomial.