Band edge localization and the density of states for acoustic and electromagnetic waves in random media
J. M. Combes, P. D. Hislop, A. Tip (1999)
Annales de l'I.H.P. Physique théorique
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J. M. Combes, P. D. Hislop, A. Tip (1999)
Annales de l'I.H.P. Physique théorique
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Frédéric Klopp (2011-2012)
Séminaire Laurent Schwartz — EDP et applications
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In the present note, we review some recent results on the spectral statistics of random operators in the localized phase obtained in []. For a general class of random operators, we show that the family of the unfolded eigenvalues in the localization region considered jointly with the associated localization centers is asymptotically ergodic. This can be considered as a generalization of []. The benefit of the present approach is that one can vary the scaling of the unfolded eigenvalues...
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.
Wei-Min Wang (2004-2005)
Séminaire Équations aux dérivées partielles
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Leonid Pastur (1991-1992)
Séminaire Bourbaki
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François Germinet, Abel Klein (2013)
Journal of the European Mathematical Society
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We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of localization at the bottom of the spectrum, which includes Anderson localization (pure point spectrum with exponentially decaying eigenfunctions) with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the...
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.