Displaying similar documents to “Localization and delocalization of random interfaces.”

On the proof of the Parisi formula by Guerra and Talagrand

Erwin Bolthausen (2004-2005)

Séminaire Bourbaki

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The Parisi formula is an expression for the limiting free energy of the Sherrington-Kirkpatrick spin glass model, which had first been derived by Parisi using a non-rigorous replica method together with an hierarchical ansatz for the solution of the variational problem. It had become quickly clear that behind the solution, if correct, lies an interesting mathematical structure. The formula has recently been proved by Michel Talagrand based partly on earlier ideas and results by Francesco...

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.

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.

The square model for random groups

Tomasz Odrzygóźdź (2016)

Colloquium Mathematicae

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We introduce a new random group model called the square model: we quotient a free group on n generators by a random set of relations, each of which is a reduced word of length 4. We prove that, just as in the Gromov model, for densities > 1/2 a random group in the square model is trivial with overwhelming probability and for densities < 1/2 a random group is hyperbolic with overwhelming probability. Moreover, we show that for densities d < 1/3 a random group in the square model...