## Probability Surveys

### On the scaling limits of weakly asymmetric bridges

Cyril Labbé

#### 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 $\alpha$.

#### Article information

Source
Probab. Surveys, Volume 15 (2018), 156-242.

Dates
First available in Project Euclid: 20 September 2018

https://projecteuclid.org/euclid.ps/1537408916

Digital Object Identifier
doi:10.1214/17-PS285

Mathematical Reviews number (MathSciNet)
MR3856167

Zentralblatt MATH identifier
06942908

#### Citation

Labbé, Cyril. On the scaling limits of weakly asymmetric bridges. Probab. Surveys 15 (2018), 156--242. doi:10.1214/17-PS285. https://projecteuclid.org/euclid.ps/1537408916

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