Weakly Asymmetric Bridges and the KPZ Equation
Labbé, Cyril (2017), Weakly Asymmetric Bridges and the KPZ Equation, Communications in Mathematical Physics, 353, 3, p. 1261 - 1298. 10.1007/s00220-017-2875-0
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1603.03560
Journal nameCommunications in Mathematical Physics
1261 - 1298
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)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−α with α∈(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 α∈(0,1/3]. In the particular regime α=1/3, these KPZ fluctuations suddenly vanish at a deterministic time.
Subjects / Keywordsstochastic heat equation; Burgers equation; exclusion process; Kardar-Parisi-Zhang equation; asymmetry; discrete bridge; height function
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