Displaying similar documents to “Eigenvalue distribution of random operators and matrices”

On Bernoulli decomposition of random variables and recent various applications

François Germinet (2007-2008)

Séminaire Équations aux dérivées partielles

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In this review, we first recall a recent Bernoulli decomposition of any given non trivial real random variable. While our main motivation is a proof of universal occurence of Anderson localization in continuum random Schrödinger operators, we review other applications like Sperner theory of antichains, anticoncentration bounds of some functions of random variables, as well as singularity of random matrices.

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.

Supersymmetry, Witten complex and asymptotics for directional Lyapunov exponents in 𝐙 d

Wei-Min Wang (1999)

Journées équations aux dérivées partielles

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By using a supersymmetric gaussian representation, we transform the averaged Green's function for random walks in random potentials into a 2-point correlation function of a corresponding lattice field theory. We study the resulting lattice field theory using the Witten laplacian formulation. We obtain the asymptotics for the directional Lyapunov exponents.

Infinite products of random matrices and repeated interaction dynamics

Laurent Bruneau, Alain Joye, Marco Merkli (2010)

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

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Let be a product of independent, identically distributed random matrices , with the properties that is bounded in , and that has a deterministic (constant) invariant vector. Assume that the probability of having only the simple eigenvalue 1 on the unit circle does not vanish. We show that is the sum of a fluctuating and a decaying process. The latter converges to zero almost surely, exponentially fast as →∞. The fluctuating part converges...