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A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit. (English) Zbl 1179.60068
The authors use the logarithmic Sobolev inequalities (LSI) to deal with the coarse-graining of a lattice system with continuous spin variable, and one provides general conditions in order that a probability measure satisfies a LSI, from there one obtains a criterion for hydrodynamic limit. As an application example, one derives a LSI for a system of spins interacting by Kawasaki dynamics with a Ginzburg-Landau-type potential.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J25 Continuous-time Markov processes on general state spaces
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
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