99-275 N.Cancrini, F.Martinelli

On the spectral gap of Kawasaki dynamics under a mixing condition revisited (134K, Plain Tex) Jul 22, 99

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Abstract. We consider a conservative stochastic spin exchange dynamics which is reversible with respect the canonical Gibbs measure of a lattice gas model. We assume that the corresponding grand canonical measure satisfies a suitable strong mixing condition. We give an alternative and quite natural, from the physical point of view, proof of the famous Lu--Yau result which states that the relaxation time in a box of side $L$ scales like $L^2$. We then show how to use such an estimate to prove a decay to equilibrium for local functions of the form ${1\over t^{\a -\e}}$ where $\e$ is positive and arbitrarily small and $\a = \ov2$ for $d=1$, $\a=1$ for $d\ge 2$.

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