Stochastic processes and random matrices : lecture notes of the Les Houches Summer School First Edition Altland

Stochastic processes and random matrices : lecture notes of the Les Houches Summer School First Edition Altland – Ebook Instant Download/Delivery ISBN(s): 9780191838774,0191838772,9780192517869, 0192517864

Product details:

• ISBN 10:0192517864
• ISBN 13: 9780192517869
• Author:Grégory Schehr; Alexander Altland; Yan V. Fyodorov
  

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).

Table contents:

1:History, Oriol Bohigas
2:Integrable Probability: Stochastic Vertex Models and Symmetric Functions
3:Free Probability
4:The Kardar-Parisi-Zhang Equation: A Statistical Physics Perspective
5:Random Matrix Theory and Quantum Chromodynamics
6:Random Matrix Theory and (Big) Data Analysis
7:Random Matrices and Loop Equations
8:Random Matrices and Number Theory: Some Recent Themes
9:Modern Telecommunications: A Playground for Physicists?
10:Random Matrix Approaches to Open Quantum Systems
11:Impurity Models and Products of Random Matrices, Alain Comtet
12:Gaussian Multiplicative Chaos and Lioville Quantum Gravity
13:Quantum Spin Chains and Classical Integrable Systems

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