守恒随机偏微分方程与对称简单排斥过程的涨落
概率论
2024-01-19 v2 偏微分方程分析
摘要
在本文中，我们为对称简单排斥过程围绕其流体力学极限的涨落提供了一个连续统模型。该模型基于一个具有非线性、守恒噪声的随机偏微分方程逼近序列。在小噪声极限下，我们证明解的涨落在一阶上等同于粒子系统涨落。此外，该 SPDE 正确地模拟了粒子过程中的稀有事件。我们证明解满足零噪声大偏差原理，其速率函数等于描述对称简单排斥过程偏离其流体力学极限的速率函数。
引用
@article{arxiv.2012.02126,
title = {Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process},
author = {Nicolas Dirr and Benjamin Fehrman and Benjamin Gess},
journal= {arXiv preprint arXiv:2012.02126},
year = {2024}
}
备注
The paper has been entirely rewritten. Our methods now treat the SPDE analogue of the SSEP, including square root noise coefficients, and establish a novel a priori estimate in $L^\infty$ for the solutions. We have also added a new section that includes numerical simulations