Transfer operator approach to 1D random band matrices

Mariya Shcherbina, Tatjana Shcherbina

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

Abstract

We discuss an application of the transfer operator approach to the analysis of the different spectral characteristics of 1d random band matrices (correlation functions of characteristic polynomials, density of states, spectral correlation functions). We show that when the bandwidth W crosses the threshold W = N 1/2, the model has a kind of phase transition (crossover), whose nature can be explained by the spectral properties of the transfer operator.

Original languageEnglish (US)
Title of host publicationInvited Lectures
EditorsBoyan Sirakov, Paulo Ney de Souza, Marcelo Viana
PublisherWorld Scientific Publishing Co. Pte Ltd
Pages2705-2727
Number of pages23
ISBN (Electronic)9789813272927
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
Volume3

Conference

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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  • Cite this

    Shcherbina, M., & Shcherbina, T. (2018). Transfer operator approach to 1D random band matrices. In B. Sirakov, P. N. de Souza, & M. Viana (Eds.), Invited Lectures (pp. 2705-2727). (Proceedings of the International Congress of Mathematicians, ICM 2018; Vol. 3). World Scientific Publishing Co. Pte Ltd.