From ABC to KPZ.

IF 1.5 1区 数学 Q2 STATISTICS & PROBABILITY
Probability Theory and Related Fields Pub Date : 2025-01-01 Epub Date: 2024-10-22 DOI:10.1007/s00440-024-01314-z
G Cannizzaro, P Gonçalves, R Misturini, A Occelli
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引用次数: 0

Abstract

We study the equilibrium fluctuations of an interacting particle system evolving on the discrete ring with N N points, denoted by T N , and with three species of particles that we name AB and C, but such that at each site there is only one particle. We prove that proper choices of density fluctuation fields (that match those from nonlinear fluctuating hydrodynamics theory) associated to the (two) conserved quantities converge, in the limit N , to a system of stochastic partial differential equations, that can either be the Ornstein-Uhlenbeck equation or the Stochastic Burgers equation. To understand the cross interaction between the two conserved quantities, we derive a general version of the Riemann-Lebesgue lemma which is of independent interest.

从ABC转到KPZ。
我们研究了在离散环上演化的相互作用粒子系统的平衡涨落,该系统有N∈N个点,记作tn,有三种粒子,分别命名为A、B和C,但在每个点上只有一个粒子。我们证明了与(两个)守恒量相关的密度涨落场的适当选择(与非线性涨落流体力学理论相匹配)在极限N→∞下收敛于随机偏微分方程系统,该系统可以是Ornstein-Uhlenbeck方程或随机Burgers方程。为了理解两个守恒量之间的交叉相互作用,我们推导出黎曼-勒贝格引理的一般版本,这是一个独立的兴趣。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Probability Theory and Related Fields
Probability Theory and Related Fields 数学-统计学与概率论
CiteScore
3.70
自引率
5.00%
发文量
71
审稿时长
6-12 weeks
期刊介绍: Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.
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