97-649 Helffer B.

Remarks on decay of correlations and Witten Laplacians III\\ --Applications to logarithmic Sobolev inequalities-- (40K, LATEX) Dec 26, 97

Abstract , Paper (src), View paper (auto. generated ps), Index 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 mechanics. 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 enough.

Files: 97-649.tex