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On the Central Limit Theorem for Stationary Mixing Random Fields
A simple proof of a central limit theorem for stationary random fields under mixing conditions is given, generalizing some results obtained by more complicated methods, e.g. Bernstein's method.
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On Ruelle's Probability Cascades and an Abstract Cavity Method
Abstract: We construct in this work a Markov process which describes a clustering mechanism through which equivalence classes on ℕ are progressively lumped together. This clustering process gives aExpand
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Entropic repulsion and the maximum of the two-dimensional harmonic crystal
We consider the lattice version of the free field in two dimensions (also called harmonic crystal). The main aim of the paper is to discuss quantitatively the entropic repulsion of the random surfaceExpand
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A central limit theorem for two-dimensional random walks in random sceneries
Let $S_n$, $n\in\bold N$, be a recurrent random walk on ${\bold Z}^2$ $(S_0=0)$ and let $\xi(\alpha)$, $\alpha\in{\bold Z}^2$, be i.i.d. $\bold R$-valued centered random variables. It is shown thatExpand
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On the Satic and Dynamic Points of View for Certain Random Walks in Random Environment
In this work we prove the equivalence between static and dynamic points of views for certain ballistic random walks in random environment on Zd, when d greater than or equal to 4 and the disorder isExpand
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Ten Lectures on Random Media
This monograph grew out of the DMV Lectures on Random Media held by the authors at the Mathematical Research Institute in Oberwolfach in November 1999 and tries to give an account of some of the developments in the field, especially in the area of random motions in random media and mean-field spin glasses. Expand
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A note on the diffusion of directed polymers in a random environment
A simple martingale argument is presented which proves that directed polymers in random environments satisfy a central limit theorem ford≧3 and if the disorder is small enough. This simplifies andExpand
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