97-584 Helffer B.

Remarks on decay of correlations and Witten Laplacians -- Brascamp-Lieb inequalities and semiclassical limit -- (39K, LATEX) Nov 19, 97

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Abstract. As it appears in recent articles by Helffer or Sj\"ostrand 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.

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