A LOGARITHMIC SOBOLEV INEQUALITY FOR ANINTERACTING SPIN SYSTEM UNDER A GEOMETRICREFERENCE MEASURE

摘要

Logarithmic Sobolev inequalities are an essential tool in the study of interacting particle systems, cf. e.g. [4, 5]. In this note we show that the logarithmic Sobolev inequality proved on the configuration space N~z~d under Poisson reference measures in [1] can be extended to geometric reference measures using the results of [2]. As a corollary we obtain a deviation estimate for an interacting particle system.