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- W2067541330 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 ∞ of the single-spin phase and when the nearest neighbor interaction is small enough. Ce travail est la continuation de deux autres articles consacrés à l'utilisation des Laplaciens de Witten dans l'analyse des intégrales de Laplace dans le contexte de la mécanique statistique. La principale application traitée dans le premier était de nature semi-classique. Dans le deuxième, on donnait des estimations très explicites dans le cas du modèle quartique. Nous abordons ici l'étude des liens avec l'inégalité de Log-Sobolev par l'intermédiaire d'un critère de B. Zegarlinski. Plus précisément, notre contribution principale est de montrer comment contrôler la décroissance des corrélations uniformément par rapport à divers paramètres sous une hypothèse très naturelle de convexité à l'infini sur la phase à un spin et lorsque l'interaction (supposée aux proches voisins) est assez petite." @default.
- W2067541330 created "2016-06-24" @default.
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- W2067541330 date "1999-07-01" @default.
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- W2067541330 title "Remarks on decay of correlations and Witten Laplacians III. Application to logarithmic Sobolev inequalities" @default.
- W2067541330 doi "https://doi.org/10.1016/s0246-0203(99)00103-x" @default.
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