On the scaling limits of weakly asymmetric bridges

Abstract

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 $\alpha$.

Survey paper based on the first version of arXiv:1603.03560

References in corpus (5)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• KPZ equation limit of higher-spin exclusion processes
• Weakly asymmetric bridges and the KPZ equation
• ASEP(q,j) converges to the KPZ equation
• Scaling limits of weakly asymmetric interfaces

Cited by in corpus (2)

• Weakly asymmetric bridges and the KPZ equation
• ASEP(q,j) converges to the KPZ equation