The Local Poincaré Inequality of Stochastic Dynamic and Application to the Ising Model  

作　　者：Kai-yuan CUI Fu-zhou GONG 

机构地区：[1]不详

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第2期305-336,共32页应用数学学报(英文版)

基　　金：supported by the National Natural Science Foundation of China(No.12288201).

摘　　要：Inspired by the idea of stochastic quantization proposed by Parisi and Wu,we reconstruct the transition probability function that has a central role in the renormalization group using a stochastic differential equation.From a probabilistic perspective,the renormalization procedure can be characterized by a discretetime Markov chain.Therefore,we focus on this stochastic dynamic,and establish the local Poincaré inequality by calculating the Bakry-Émery curvature for two point functions.Finally,we choose an appropriate coupling relationship between parameters K and T to obtain the Poincaré inequality of two point functions for the limiting system.Our method extends the classic Bakry-Émery criterion,and the results provide a new perspective to characterize the renormalization procedure.

关 键 词：Ising model stochastic quantization local Poincaréinequality Bakry-Émery curvature RENORMALIZATION 

分 类 号：O211[理学—概率论与数理统计]