Stochastic Burgers equation from long range exclusion interactions

We consider one-dimensional exclusion processes with long jumps given by a transition probability of the form pn(⋅)=s(⋅)+γna(⋅), 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 nγn→n→∞b≠0, the equilibrium density fluctuations are given by the unique energy solution of the stochastic Burgers equation.