Hydrodynamic limit for a $d$-dimensional open symmetric exclusion process

Abstract

In this paper we focus on the open symmetric exclusion process with parameter $m$ (open SEP($m/2$)), which allows $m$ particles each site and has an open boundary. We generalize the result about hydrodynamic limit for the open SEP$(m/2)$ originally raised in Theorem 4.12 of [8]. We prove that the hydrodynamic limit of the density profile for a $d$-dimensional open SEP$(m/2)$ solves the $(d+1)$-dimensional heat equation with certain initial condition and boundary condition.