Approach to Equilibrium in the Symmetric Simple Exclusion Process

#### N. Cancrini, A. Galves

1995, v.1, Issue 2, 175-184

ABSTRACT

We obtain an upper bound for the rate of convergence to equilibrium of the $d$-dimensional simple symmetric exclusion process starting either with a periodic configuration or with a stationary mixing probability distribution. More precisely, denoting this process by $\eta^*_t$, we will show that for all $t$ large enough $$\left\vert {\sf P}\left\{\eta^*_t\in Y_N\right\} - \rho^{N} \right\vert \le c_{d} ~N^2\bigl({\log t \over \sqrt {t}}\bigr)^d,$$ where $Y_N$ is the cylindrical set with all $N$ sites of the corresponding box being occupied.

Keywords: symmetric simple exclusion process,convergence rate