 99275 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 LuYau 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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