Diffusive Long-time Behavior of Kawasaki Dynamics

Abstract

If $P_t$ is the semigroup associated with the Kawasaki dynamics on $Z^d$ and $f$ is a local function on the configuration space, then the variance with respect to the invariant measure $\mu$ of $P_t f$ goes to zero as $t\to \infty$ faster than $t^{-d/2+\varepsilon}$, with $\varepsilon$ arbitrarily small. The fundamental assumption is a mixing condition on the interaction of Dobrushin and Schlosman type.