
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
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Article accepté pour publication ou publiéExternal document link
https://arxiv.org/abs/1603.03560Date
2017Journal name
Communications in Mathematical PhysicsVolume
353Number
3Publisher
Springer
Pages
1261 - 1298
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Metadata
Show full item recordAbstract (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 / Keywords
stochastic heat equation; Burgers equation; exclusion process; Kardar-Parisi-Zhang equation; asymmetry; discrete bridge; height functionRelated items
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