Stochastic Burgers equation from long range exclusion interactions

2016/06/21 by Gonçalves, Patricia, Jara, Milton
#60K35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1606.06655

Abstract

We consider one-dimensional exclusion processes with long jumps given by a transition probability of the form p_n(⋅)=s(⋅)+γ_na(⋅), such that its symmetric part s(⋅) is irreducible with finite variance and its antisymmetric part is absolutely bounded by s(⋅). We prove that under diffusive time scaling and strength of asymmetry √ n γ_n →_n→∞ b≠ 0, the equilibrium density fluctuations are given by the unique energy solution of the stochastic Burgers equation.

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