Crossover to the stochastic Burgers equation for the WASEP with a slow bond

Abstract : We consider the weakly asymmetric simple exclusion process in the presence of a slow bond and starting from the invariant state, namely the Bernoulli product measure of parameter ρ∈(0,1). The rate of passage of particles to the right (resp. left) is 12+a2nγ (resp. 12−a2nγ) except at the bond of vertices {−1,0} where the rate to the right (resp. left) is given by α2nβ+a2nγ (resp. α2nβ−a2nγ). Above, α>0, γ≥β≥0, a≥0. For β<1, we show that the limit density fluctuation field is an Ornstein-Uhlenbeck process defined on the Schwartz space if γ>12, while for γ=12 it is an energy solution of the stochastic Burgers equation. For γ≥β=1, it is an Ornstein-Uhlenbeck process associated to the heat equation with Robin's boundary conditions. For γ≥β>1, the limit density fluctuation field is an Ornstein-Uhlenbeck process associated to the heat equation with Neumann's boundary conditions.
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https://hal.inria.fr/hal-01355447
Contributor : Marielle Simon <>
Submitted on : Tuesday, August 23, 2016 - 1:06:44 PM
Last modification on : Thursday, March 28, 2019 - 3:21:54 PM

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Tertuliano Franco, Patricia Goncalves, Marielle Simon. Crossover to the stochastic Burgers equation for the WASEP with a slow bond. Communications in Mathematical Physics, Springer Verlag, 2016, ⟨10.1007/s00220-016-2607-x⟩. ⟨hal-01355447⟩

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