First order correction for the hydrodynamic limit of symmetric simple exclusion processes with speed change in dimension $d\geq 3$

Abstract

The hydrodynamic limit of the symmetric simple exclusion process with speed change is given by a diffusive equation in the appropriate scale. Following the nongradient method introduced by Varadhan and the Navier-Stokes methods developed by Yau, we prove that in the same scale, the next order correction is given by a third order equation for dimension $d \geq 3$.