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 (alphain(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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