10.1007/s00220-016-2600-4
Sadel, Christian
Christian
Sadel0000-0001-8255-3968
Virág, Bálint
Bálint
Virág
A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes
Springer
2016
2018-12-11T11:50:59Z
2020-01-16T12:35:46Z
journal_article
https://research-explorer.app.ist.ac.at/record/1257
https://research-explorer.app.ist.ac.at/record/1257.json
800792 bytes
application/pdf
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.