Abstract

In the last two lectures of this mini-course we will prove that the density profile of the exclusion process evolves according to the solution of a non-linear parabolic equation.

We first will examine the stationary states of the exclusion process and then their thermodynamic limit. This will lead us to define local equilibrium states. Then, starting from a local equilibrium state, we will prove for two different models, the so-called simple exclusion process and the gradient exclusion processes, that the density profile which characterizes the local equilibrium state

evolves according to a non-linear parabolic equation.

(This is a continuation of the first session of the mini-course on March 13.)