Abstract

We consider a conservative stochastic spin exchange dynamics, reversible with respect to the canonical Gibbs measure of a lattice gas model. We assume that the corresponding grand canonical measure satisfies a suitable strong mixing condition. We discuss the main ideas we used to re-prove the well-known results of Lu and Yau, and of Yau stating that the inverse of the spectral gap and the logarithmic Sobolev constant in a box of sideLgrow likeL 2.

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