Remarks on decay of correlations and Witten Laplacians Brascamp-Lieb inequalities and semiclassical limit

摘要

As it appears in recent articles by Helffer or Sjostrand and Naddaf-Spencer, the analysis, in the context of the statistical mechanics, of measures of the type exp - Phi(x)dx is connected with the analysis of suitable Witten Laplacians on 1-forms. For illustrating this point of view, we present here remarks about the Brascamp-Lieb inequalities and its extensions and prove the decay of the correlation in some cases when Phi is weakly non convex. (C) 1998 Academic Press. [References: 33]