Random band matrices - Paul Bourgade - ICM2018

Probability and Statistics
Invited Lecture 12.2
Random band matrices
Paul Bourgade
Abstract: We survey recent mathematical results about the spectrum of random band matrices. We start by exposing the Erdős-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.
ICM 2018 - International Congress of Mathematicians ©
www.icm2018.org
Os direitos sobre todo o material deste canal pertencem ao Instituto de Matemática Pura e Aplicada, sendo vedada a utilização total ou parcial do conteúdo sem autorização prévia e por escrito do referido titular, salvo nas hipóteses previstas na legislação vigente.
The rights over all the material in this channel belong to the Instituto de Matemática Pura e Aplicada, and it is forbidden to use all or part of it without prior written authorization from the above mentioned holder, except in the cases prescribed in the current legislation.