Open Access
Translator Disclaimer
2019 A forward-backward random process for the spectrum of 1D Anderson operators
Raphael Ducatez
Electron. Commun. Probab. 24: 1-13 (2019). DOI: 10.1214/19-ECP232

Abstract

We give a new expression for the law of the eigenvalues of the discrete Anderson model on the finite interval $[1,N]$, 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 $\gamma , \sigma >0 $, $B_{s}$ is the Brownian motion and $k$ is uniformly chosen in $[1,N]$ 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 $\frac{1} {\sqrt{N} }$.

Citation

Download Citation

Raphael Ducatez. "A forward-backward random process for the spectrum of 1D Anderson operators." Electron. Commun. Probab. 24 1 - 13, 2019. https://doi.org/10.1214/19-ECP232

Information

Received: 20 February 2018; Accepted: 16 April 2019; Published: 2019
First available in Project Euclid: 7 November 2019

zbMATH: 07142640
MathSciNet: MR4029438
Digital Object Identifier: 10.1214/19-ECP232

Subjects:

JOURNAL ARTICLE
13 PAGES


SHARE
Back to Top