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On the scaling limits of weakly asymmetric bridges
Cyril Labbé · 2016-09-19 · via math.PR updates on arXiv.org

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 $N^{-α}$ with $α\in (0,\infty)$. We provide a classification of the asymptotic behaviours - invariant measure, hydrodynamic limit and fluctuations - of this model according to the value of the parameter $α$.

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