Random band matrices
Probability
2018-08-31 v2 Mathematical Physics
math.MP
Abstract
We survey recent mathematical results about the spectrum of random band matrices. We start by exposing the Erd{\H o}s-Schlein-Yau dynamic approach, its application to Wigner matrices, and extension to other mean-field models. We then introduce random band matrices and the problem of their Anderson transition. We finally describe a method to obtain delocalization and universality in some sparse regimes, highlighting the role of quantum unique ergodicity.
Cite
@article{arxiv.1807.03031,
title = {Random band matrices},
author = {Paul Bourgade},
journal= {arXiv preprint arXiv:1807.03031},
year = {2018}
}
Comments
Proceedings ICM 2018, Rio de Janeiro