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A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit

Natalie GrunewaldFelix OttoCédric VillaniMaria G. Westdickenberg — 2009

Annales de l'I.H.P. Probabilités et statistiques

We consider the coarse-graining of a lattice system with continuous spin variable. In the first part, two abstract results are established: sufficient conditions for a logarithmic Sobolev inequality with constants independent of the dimension (Theorem 3) and sufficient conditions for convergence to the hydrodynamic limit (Theorem 8). In the second part, we use the abstract results to treat a specific example, namely the Kawasaki dynamics with Ginzburg–Landau-type potential.

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