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Étude asymptotique de certains systèmes désordonnés

Abstract : This thesis basically study two kinds of disorder systems. The first one the spin glasses and second one the directed polymers into a random environment. These two research themes can be solved by the utilization of the same tools. Although they are strongly different by the nature of the interactions and the geometry structure that they create. In few words, we give a summary: For the Sherrington-Kirkpatrick Spin Glasses model, we make an asymptotic study of the multiple overlap function which generalizes the typical two configuration overlap function. Afterward, we develop a central limit theorem for the partition function of a localized Sherrigton-Kirkpatrick model. At the end, we obtain a study of the partition function and a result of super-diffusivity for a brownien directed polymer model into an random gaussian environment.
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Submitted on : Thursday, March 29, 2018 - 11:30:14 AM
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  • HAL Id : tel-01748271, version 1



Sérgio De Carvalho Bezerra. Étude asymptotique de certains systèmes désordonnés. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2007. Français. ⟨NNT : 2007NAN10053⟩. ⟨tel-01748271⟩



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