On the scaling limits of weakly asymmetric bridges

Probability Surveys

Cyril Labbé¹ 

关键词: Exclusion process;    height function;    bridge;    stochastic heat equation;    Burgers equation;    KPZ equation;   

DOI  :  10.1214/17-PS285

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

We consider a discrete bridge from $(0,0)$ to $(2N,0)$ evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order $N^{-\alpha}$ with $\alpha\in(0,\infty)$. We provide a classification of the asymptotic behaviours - invariant measure, hydrodynamic limit and fluctuations - of this model according to the value of the parameter $\alpha$.

【 授权许可】

Free