Stochastic Processes And Random Matrices
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Stochastic Processes and Random Matrices
Author: Grégory Schehr
language: en
Publisher: Oxford University Press
Release Date: 2017-08-15
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).
An Introduction to Random Matrices
Author: Greg W. Anderson
language: en
Publisher: Cambridge University Press
Release Date: 2010
A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.
Stochastic Processes and Random Matrices
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. This volume not only covers this topic in detail but also presents more recent developments that have emerged.