Displaying similar documents to “Huge random structures and mean field models for spin glasses.”

A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach

Sébastien Breteaux (2014)

Annales de l’institut Fourier

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In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.

Superdiffusivity for directed polymer in corelated random environment

Hubert Lacoin (2010)

Actes des rencontres du CIRM

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The directed polymer in random environment models the behavior of a polymer chain in a solution with impurities. It is a particular case of random walk in random environment. In 1 + 1 dimensional environment is has been shown by Petermann that this random walk is superdiffusive. We show superdiffusivity properties are reinforced were there are long ranged correlation in the environment and that super diffusivity also occurs in higher dimensions.

Strong disorder in semidirected random polymers

N. Zygouras (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called Lyapounov norms. We identify situations where the point-to-hyperplane annealed and quenched Lyapounov norms are different. We also prove that in these cases the polymer path exhibits localization.

Lifshitz tails for some non monotonous random models

Frédéric Klopp, Shu Nakamura (2007-2008)

Séminaire Équations aux dérivées partielles

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In this talk, we describe some recent results on the Lifshitz behavior of the density of states for non monotonous random models. Non monotonous means that the random operator is not a monotonous function of the random variables. The models we consider will mainly be of alloy type but in some cases we also can apply our methods to random displacement models.