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

Abstract

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. © 2009 Association des Publications de l'Institut Henri Poincaré.