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Theses

Asymptotique des propriétés locales pour le modèle d'Ising et applications

Abstract : This thesis intends to study local properties satisfied by the Ising model defined on a d-dimensional lattice torus. As the size n of the lattice tends to infinity, a limit for their probability of occurring is obtained depending on the surface potential a=a(n) and the pair potential b=b(n). By establishing a threshold phenomenon, we determine the moment from which a given local property occurs in the lattice. Thus, at its threshold function, we prove a poisson approximation for its probability of occurring. Finally, two applications are proposed: an estimate of potentials a and b and a denoising algorithm for grey level images.
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https://tel.archives-ouvertes.fr/tel-00011136
Contributor : David Coupier <>
Submitted on : Wednesday, November 30, 2005 - 4:31:57 PM
Last modification on : Friday, April 10, 2020 - 5:20:50 PM
Long-term archiving on: : Friday, April 2, 2010 - 11:17:34 PM

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David Coupier. Asymptotique des propriétés locales pour le modèle d'Ising et applications. Mathématiques [math]. Université René Descartes - Paris V, 2005. Français. ⟨tel-00011136⟩

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