DIFFUSIVE LIMIT OF ASYMMETRIC SIMPLE EXCLUSION

Abstract

We consider the asymmetric simple exclusion process on the lattice [Formula: see text] with periodic b.c. for d ≥ 3, in the diffusive space-time scaling with parameter ε. Assume the initial state is a product of Bernoulli measures with density of order ε, up to a fixed reference constant density θ. We prove that the density at time t is given to first order by θ − εm(x − ε−1vt, t) with v a uniform velocity depending on θ and the dynamics and m(z, t) satisfies the d-dimensional viscous Burgers equation. The diffusion matrix is given by a variational formula related to the Green-Kubo formula and it is strictly bigger than the diffusion matrix for the corresponding symmetric exclusion process.