93-211 Esposito R., Marra R., YAU H. T.

Diffusive limit of asymmetric simple exclusion (104K, Latex/documentstyle_article) Jul 30, 93

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Abstract. We consider the asymmetric simple exclusion process on the lattice ${\cal Z}^d\cap T^d$ with periodic b.c. for $d\ge 3$, in the diffusive space-time scaling with parameter $\e$. Assume the initial state is a product of Bernoulli measures with density of order $\e$, up to a fixed reference constant density $\theta$. We prove that the density at time $t$ is given to first order by $\theta - \e m(x-\e^{-1}vt,t)$ with $v$ a uniform velocity depending on $\theta$ 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.

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