- 97-584 Helffer B.
- Remarks on decay of correlations and Witten Laplacians
-- Brascamp-Lieb inequalities and semiclassical limit --
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.