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Applications d'inégalités fonctionnelles à la mécanique statistique et au recuit simulé

Abstract : In this work, we apply several functional inequalities (Poincaré,
logarithmic Sobolev etc.) to solve two problems. First, we study an
inhomogeneous diffusion, akin to the discrete simulated annealing
algorithm, in the spirit of a paper by L. Miclo. We show that this
diffusion converges under weaker hypotheses than what was assumed in
previous work. In particular, the potential governing the drift is
allowed to grow very slowly at infinity. In a second part, we turn to
a model of statistical mechanics with unbounded spins, recently
studied by T. Bodineau and B. Helffer, N. Yoshida and G. Royer (among
others). We clarify links between mixing properties, uniqueness of the
Gibbs measure, and functional inequalities. We show in particular that
the infinite volume tempered Gibbs measure is unique, provided that
the finite volume measures for one boundary condition satisfy a
Beckner inequality.
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https://tel.archives-ouvertes.fr/tel-00114033
Contributor : Pierre-André Zitt <>
Submitted on : Monday, January 8, 2007 - 3:46:32 PM
Last modification on : Tuesday, March 2, 2021 - 9:59:30 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 10:44:02 PM

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  • HAL Id : tel-00114033, version 1

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Pierre-André Zitt. Applications d'inégalités fonctionnelles à la mécanique statistique et au recuit simulé. Mathématiques [math]. Université de Nanterre - Paris X, 2006. Français. ⟨tel-00114033⟩

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