N.Cancrini, F.Martinelli
 On the spectral gap of Kawasaki dynamics 
under a mixing condition revisited
(134K, Plain Tex)

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 
$d\ge 2$.