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Pré-Publication, Document De Travail Année : 2017

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

Résumé

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 $\exp(\sigma B_{|n-k|}-\gamma\frac{|n-k|}{4})$ where $B_{s}$ is the Brownian motion and $k$ is uniformly chosen in $[0,N]$ independently of $B_{s}$. 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 $\frac{1}{\sqrt{N}}$
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Dates et versions

hal-01651812 , version 1 (29-11-2017)

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Raphael Ducatez. A forward–backward random process for the spectrum of 1D Anderson operators. 2017. ⟨hal-01651812v1⟩
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