- 97-649 Helffer B.
- Remarks on decay of correlations and Witten Laplacians III\\
--Applications to logarithmic Sobolev inequalities--
Dec 26, 97
(auto. generated ps),
of related papers
Abstract. This is the continuation of our two previous articles devoted to the use of
Witten Laplacians for analyzing Laplace integrals in statistical
The main application treated in Part I was a semi-classical one.
The second application was more perturbative in spirit and gave very
explicit estimates for the lower bound of the Witten Laplacian in the
case of a quartic model.
We shall relate in this third part our studies of the Witten Laplacian
with the existence of uniform logarithmic Sobolev inequalities
through a criterion of B. Zegarlinski.
More precisely, our main contribution is to show how to control the
decay of correlations uniformly with respect to various parameters,
under a natural condition of strict convexity at $\infty$ of the
single-spin phase and when the nearest neighbor interaction is small