ISBN : 9780198797319
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).
1 Oriol Bohigas, Hans Weidenmuller: History
2 Alexei Borodin, Leonid Petrov: Integrable Probability: Stochastic Vertex Models and Symmetric Functions
3 Alice Guionnet: Free Probability
4 Herbet Spohn: The Kardar-Parisi-Zhang Equation: A Statistical Physics Perspective
5 Gernot Akemann: Random Matrix Theory and Quantum Chromodynamics
6 Jean-Philippe Bouchaud: Random Matrix Theory and (Big) Data Analysis
7 Bertrand Eynard: Random Matrices and Loop Equations
8 Jon P. Keating: Random Matrices and Number Theory: Some Recent Themes
9 Aris L. Moustakas: Modern Telecommunications: A Playground for Physicists?
10 Henning Schomerus: Random Matrix Approaches to Open Quantum Systems
11 Alain Comtet, Yves Tourigny: Impurity Models and Products of Random Matrices
12 Remi Rhodes, Vincent Vargas: Gaussian Multiplicative Chaos and Lioville Quantum Gravity
13 Anton Zabrodin: Quantum Spin Chains and Classical Integrable Systems