King's College London

Research portal

Stochastic processes and random matrices: Lecture notes of the Les Houches summer school

Research output: Book/ReportBook

Grégory Schehr, Alexander Altland, Yan V. Fyodorov, Neil O'Connell, Leticia F. Cugliandolo

Original languageEnglish
PublisherOxford University Press
Number of pages613
Volume104
ISBN (Print)9780198797319
DOIs
Publication statusPublished - 18 Jan 2018

King's Authors

Abstract

The field of stochastic processes and Random Matrix Theory (RMT) has been a rapidly evolving subject during the last fifteen years. The continuous development and discovery of new tools, connections and ideas have led to an avalanche of new results. These breakthroughs have been made possible thanks, to a large extent, to the recent development of various new techniques in RMT. Matrix models have been playing an important role in theoretical physics for a long time and they are currently also a very active domain of research in mathematics. An emblematic example of these recent advances concerns the theory of growth phenomena in the Kardar-Parisi-Zhang (KPZ) universality class where the joint efforts of physicists and mathematicians during the last twenty years have unveiled the beautiful connections between this fundamental problem of statistical mechanics and the theory of random matrices, namely the fluctuations of the largest eigenvalue of certain ensembles of random matrices. This text not only covers this topic in detail but also presents more recent developments that have emerged from these discoveries, for instance in the context of low dimensional heat transport (on the physics side) or integrable probability (on the mathematical side).

View graph of relations

© 2018 King's College London | Strand | London WC2R 2LS | England | United Kingdom | Tel +44 (0)20 7836 5454