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 Probability Surveys > Vol. 15 (2018) open journal systems 


On the scaling limits of weakly asymmetric bridges

Cyril Labbé, Université Paris Dauphine


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 \(\alpha\).

AMS 2000 subject classifications: Primary 60K35; secondary 60H15, 82C24.

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

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

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