DERIVATION OF COUPLED KPZ-BURGERS EQUATION FROM MULTI-SPECIES ZERO-RANGE PROCESSES

被引：6
|
作者：
Bernardin, C. [1 ]
Funaki, T. [2 ]
Sethuraman, S. [3 ]
机构：
[1] Univ Cote dAzur, LJAD, CNRS, Nice, France
[2] Waseda Univ, Dept Math, Sch Fundamental Sci & Engn, Tokyo, Japan
[3] Univ Arizona, Dept Math, Tucson, AZ 85721 USA
来源：
ANNALS OF APPLIED PROBABILITY | 2021年 / 31卷 / 04期
基金：
欧洲研究理事会; 日本学术振兴会;
关键词：
Interacting; particle system; zero-range; multi-species; weakly asymmetric; fluctuation; field; Burgers; coupled; KPZ; nonlinear fluctuating hydrodynamics; STOCHASTIC BURGERS;
D O I：
10.1214/20-AAP1639
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We consider the fluctuation fields of multi-species weakly-asymmetric zero-range interacting particle systems in one dimension, where the mass density of each species is conserved. Although such fields have been studied in systems with a single species, the multi-species setting is much less understood. Among other results, we show that when the system starts from stationary states with a particular property, the scaling limits of the multi-species fluctuation fields, seen in a characteristic traveling frame, solve a coupled Burgers SPDE, which is a formal spatial gradient of a coupled KPZ equation.
引用
收藏
页码：1966 / 2017
页数：52
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