Diffusive long-time behavior of Kawasaki dynamics

If P(t) is the semigroup asssociated 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 --> infinity faster than the t(-d/2+epsilon), with epsilon arbitrarily small. The fundamental assumption is a mixing condition on the interaction of Dobrushin and Schlosman type.