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arXiv · 1609.05617

On the scaling limits of weakly asymmetric bridges

Cyril Labbé
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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 $N^{-α}$ 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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Cyril Labbé. 2018-09-20. On the scaling limits of weakly asymmetric bridges. https://doi.org/10.1214/17-ps285

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