The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited

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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. Following previous work by two of us for the spectral gap, we provide an alternative and quite natural, from the physical point of view, proof of the well known result of Yau stating that the logarithmic Sobolev constant in a box of side L grows like L2. © 2002 Éditions scientifiques et médicales Elsevier SAS.

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Cancrini, N., Martinelli, F., & Roberto, C. (2002). The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited. Annales de l’institut Henri Poincare (B) Probability and Statistics, 38(4), 385–436. https://doi.org/10.1016/S0246-0203(01)01096-2

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