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A forward–backward random process for the spectrum of 1D Anderson operators

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Date
2017
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01651812
Dewey
Sciences connexes (physique, astrophysique)
Sujet
Anderson model; random process
URI
https://basepub.dauphine.fr/handle/123456789/17525
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Ducatez, Raphaël
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
15
Abstract (EN)
We give a new expression for the law of the eigenvalues of the discrete Anderson model on the finite interval [0,N], in terms of two random processes starting at both ends of the interval. Using this formula, we deduce that the tail of the eigenvectors behaves approximately like exp(σB|n−k|−γ|n−k|4) where Bs is the Brownian motion and k is uniformly chosen in [0,N] independently of Bs. A similar result has recently been shown by B. Rifkind and B. Virag in the critical case, that is, when the random potential is multiplied by a factor 1N√

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