Decay to Equilibrium in $L^\infty$ of Finite Interacting Particle Systems in Infinite Volume

#### C. Landim

1998, v.4, №4, 517-534

ABSTRACT

We consider $n$ particles evolving as asymmetric random walks in the lattice $Z^d$ with an exclusion rule that allows at most one particle per site. For two subsets $A$, $B$ of $Z^d$ with $n$ elements, denote by $p_t(A,B)$ the probability for the system being at time $t$ at $B$ if it started from $A$. We prove that there exists a universal constant $C=C(d,n)$ such that $p_t(A,B)\le C t^{-nd/2}$. In the case of mean zero gradient processes we obtain Gaussian estimates with logarithmic corrections of the off-diagonal terms.

Keywords: interacting particle systems,decay to equilibrium