A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes

Sadel, Christian and Virág, Bálint (2016) A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. Communications in Mathematical Physics, 343 (3). pp. 881-919. ISSN 1432-0916

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Abstract

We consider products of random matrices that are small, independent identically distributed perturbations of a fixed matrix (Formula presented.). Focusing on the eigenvalues of (Formula presented.) of a particular size we obtain a limit to a SDE in a critical scaling. Previous results required (Formula presented.) to be a (conjugated) unitary matrix so it could not have eigenvalues of different modulus. From the result we can also obtain a limit SDE for the Markov process given by the action of the random products on the flag manifold. Applying the result to random Schrödinger operators we can improve some results by Valko and Virag showing GOE statistics for the rescaled eigenvalue process of a sequence of Anderson models on long boxes. In particular, we solve a problem posed in their work.

Item Type: Article
DOI: 10.1007/s00220-016-2600-4
Subjects: 500 Science > 510 Mathematics
500 Science > 530 Physics > 539 Modern physics
Research Group: Erdös Group
SWORD Depositor: Sword Import User
Depositing User: Sword Import User
Date Deposited: 06 Dec 2016 09:01
Last Modified: 05 Sep 2017 09:43
URI: https://repository.ist.ac.at/id/eprint/703

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