Impurity models and products of random matrices

Alain Comtet, Yves Tourigny

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Abstract

This is an introduction to the theory of one-dimensional disordered systems and products of random matrices, confined to the 2 by 2 case. The notion of impurity model--- that is, a system in which the interactions are highly localised--- links the two themes and enables their study by elementary mathematical tools.
After discussing the spectral theory of some impurity models, we state and illustrate Furstenberg's theorem, which gives sufficient conditions for the exponential growth of a product of independent, identically-distributed matrices.
Original languageEnglish
Title of host publicationStochastic Processes and Random Matrices
Subtitle of host publicationLecture Notes of the Les Houches Summer School 2015
EditorsGregory Schehr, Alexander Altland, Yan V. Fyodorov, Neil O'Connell, Leticia F. Cugliandolo
Place of PublicationOxford
PublisherOxford University Press
Chapter11
Number of pages71
Volume104
ISBN (Print)9780198797319
DOIs
Publication statusPublished - 10 Aug 2017

Publication series

NameLecture Notes of the Les Houches Summer School
PublisherOUP

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