GUE×GUE limit law at hard shocks in ASEP

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-02-01 DOI:10.1214/20-AAP1591

Peter Nejjar

引用次数: 7

Abstract

We consider the asymmetric simple exclusion process (ASEP) on Z with initial data such that in the large time particle density ρ(·) a discontinuity (shock) at the origin is created. At the shock, the value of ρ jumps from zero to one, but ρ(−ε), 1−ρ(ε) > 0 for any ε > 0. We are interested in the rescaled position of a tagged particle which enters the shock with positive probability. We show that, inside the shock region, the particle position has the KPZ-typical 1/3 fluctuations, a FGUE×FGUE limit law and a degenerated correlation length. Outside the shock region, the particle fluctuates as if there was no shock. Our arguments are mostly probabilistic, in particular, the mixing times of countable state space ASEPs are instrumental to study the fluctuations at shocks.

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GUE×GUE限制法律在ASEP的硬冲击

我们用初始数据考虑Z上的不对称简单不相容过程(ASEP)，使得在大时间粒子密度ρ(·)下，在原点处产生不连续(激波)。在激波处，ρ值从0跳到1，但是ρ(−ε)， 1−ρ(ε) >对于任何ε > 0。我们感兴趣的是以正概率进入激波的标记粒子的重新缩放位置。结果表明，在激波区域内，粒子位置具有kpz -典型的1/3波动、FGUE×FGUE极限定律和简并的相关长度。在激波区域之外，粒子像没有激波一样波动。我们的论点大多是概率性的，特别是可数状态空间asep的混合时间对研究冲击时的波动是有帮助的。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.