Random band matrices

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationInvited Lectures
EditorsBoyan Sirakov, Paulo Ney de Souza, Marcelo Viana
PublisherWorld Scientific Publishing Co. Pte Ltd
Pages2777-2802
Number of pages26
ISBN (Electronic)9789813272934
StatePublished - 2018
Event2018 International Congress of Mathematicians, ICM 2018 - Rio de Janeiro, Brazil
Duration: Aug 1 2018Aug 9 2018

Publication series

NameProceedings of the International Congress of Mathematicians, ICM 2018
Volume4

Conference

Conference2018 International Congress of Mathematicians, ICM 2018
CountryBrazil
CityRio de Janeiro
Period8/1/188/9/18

Keywords

  • Band matrices
  • Delocalization
  • Gaussian free field
  • Quantum unique ergodicity

ASJC Scopus subject areas

  • Mathematics(all)

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