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Article Dans Une Revue Communications in Mathematical Physics Année : 2017

Weakly Asymmetric Bridges and the KPZ Equation

Résumé

We consider the corner growth dynamics on discrete bridges from $(0,0)$ to $(2N,0)$, or equivalently, the weakly asymmetric simple exclusion process with $N$ particles on $2N$ sites. We take an asymmetry of order $N^{-\alpha}$ with $\alpha \in (0,1)$ and provide a complete description of the asymptotic behaviour of this model. In particular, we show that the hydrodynamic limit of the density of particles is given by the inviscid Burgers equation with zero-flux boundary condition. When the interface starts from the flat initial profile, we show that KPZ fluctuations occur whenever $\alpha \in (0,1/3]$. In the particular regime $\alpha =1/3$, these KPZ fluctuations suddenly vanish at a deterministic time.

Dates et versions

hal-01288761 , version 1 (15-03-2016)

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Citer

Cyril Labbé. Weakly Asymmetric Bridges and the KPZ Equation. Communications in Mathematical Physics, 2017, 353 (3), pp.1261 - 1298. ⟨10.1007/s00220-017-2875-0⟩. ⟨hal-01288761⟩
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