Open Access
2018 On the scaling limits of weakly asymmetric bridges
Cyril Labbé
Probab. Surveys 15: 156-242 (2018). DOI: 10.1214/17-PS285


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 $\alpha$.


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Cyril Labbé. "On the scaling limits of weakly asymmetric bridges." Probab. Surveys 15 156 - 242, 2018.


Received: 1 May 2017; Published: 2018
First available in Project Euclid: 20 September 2018

zbMATH: 06942908
MathSciNet: MR3856167
Digital Object Identifier: 10.1214/17-PS285

Primary: 60K35
Secondary: 60H15 , 82C24

Keywords: bridge , Burgers equation , Exclusion process , height function , KPZ equation , Stochastic heat equation

Vol.15 • 2018
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