@inproceedings{472d00902cba49e99e7a78cc42f281b0,
title = "Random band matrices",
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 expose a method to obtain delocalization and universality in some sparse regimes, highlighting the role of quantum unique ergodicity.",
keywords = "Band matrices, Delocalization, Gaussian free field, Quantum unique ergodicity",
author = "Paul Bourgade",
note = "Publisher Copyright: {\textcopyright} ICM 2018.All rights reserved.; 2018 International Congress of Mathematicians, ICM 2018 ; Conference date: 01-08-2018 Through 09-08-2018",
year = "2018",
language = "English (US)",
series = "Proceedings of the International Congress of Mathematicians, ICM 2018",
publisher = "World Scientific Publishing Co. Pte Ltd",
pages = "2777--2802",
editor = "Boyan Sirakov and {de Souza}, {Paulo Ney} and Marcelo Viana",
booktitle = "Invited Lectures",
}