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

Ducatez, Raphaël (2019), A forward–backward random process for the spectrum of 1D Anderson operators, Electronic Communications in Probability, 24, p. 1-13. 10.1214/19-ECP232

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Electronic Communications in Probability
Volume
24
Publisher
Institute of Mathematical Statistics
Pages
1-13
Publication identifier
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Author(s)
Ducatez, Raphaël
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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√
Subjects / Keywords
Anderson model; random process