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Labbé, Cyril

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

Probab. Surv. 15, 156-242 (2018).
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 \(\alpha\).

Cited in 3 Documents

MSC:

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

Keywords:

exclusion process; height function; bridge; stochastic heat equation; Burgers equation; KPZ equation
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Full Text: DOI arXiv Euclid

References:

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