On the scaling limits of weakly asymmetric bridges. (English) Zbl 1409.60145

Summary: 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 \(\alpha\).


60K35 Interacting random processes; statistical mechanics type models; percolation theory
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
Full Text: DOI arXiv Euclid


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