The Oxford Handbook of Random Matrix Theory (Hardcover)

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。Foreword by Freeman Dyson
All main theoretical aspects and current applications of random matrices are covered
。Complementing views of leaders in the fields of mathematics and physics
。Applications in all branches of physics are covered, as well as in mathematics, biology and engineering
。Includes most important and up to date references
。Provides a guide for newcomers to the field
。Introduces those already familiar with random matrix theory with new areas of research

With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach.

In part one, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicas or supersymmetry. Further, all main extensions of the classical Gaussian ensembles of Wigner and Dyson are introduced including sparse, heavy tailed, non-Hermitian or multi-matrix models. In the second and larger part, all major applications are covered, in disciplines ranging from physics and mathematics to biology and engineering. This includes standard fields such as number theory, quantum chaos or quantum chromodynamics, as well as recent developments such as partitions, growth models, knot theory, wireless communication or bio-polymer folding.

The handbook is suitable both for introducing novices to this area of research and as a main source of reference for active researchers in mathematics, physics and engineering.

Table Of Contents

Freeman Dyson: Forward

I Introduction

1: Gernot Akenmann, Jinho Baik & Philippe Di Francesco: Guide to the Handbook

2: Oriol Bohigas & Hans Weidenmu"ller: History

II Properties of Random Matrix Theory

3: Martin Zirnbauer: Symmetry Classes

4: Greg W. Anderson: Spectral Statisitics of Unitary Emsembles

5: Mark Adler: Spectral Statistics of Orthogonal and Symplectic Ensembles

6: Arno Kuijlaars: Universality

7: Thomas Guhr: Supersymmetry

8: Eugene Kanzieper: Replica Approach

9: Alexander Its: Painleve' Transcendents

10: Pierre van Moerbeke: Random Matrices and Integrable Systems

11: Alexei Borodin: Determinantal Point Processes

12: Vladimir Kravtsov: Random Matrix Representations of Critical Statistics

13: Zdzislaw Burda & Jerzy Jurkiewicz: Heavy-Tailed Random Matrices

14: Giovanni Cicuta & Luca Molinari: Phase Transitions

15: Marco Bertola: Two-Matrix Models and Biorthogonal Polynomials

16: Nicolas Orantin: Loop Equation Method

17: Alexei Morozov: Unitary Integrals and Related Matrix Models

18: Boris Khoruzhenko & Hans-Ju"rgen Sommers: Non-Hermitian Ensembles

19: Edouard Bre'zin & Sinobu Hikami: Characteristic Polynomials

20: Peter Forrester: Beta Ensembles

21: Ge'rard Ben Arous & Guionnet: Wigner Matrices

22: Roland Speicher: Free Probability Theory

23: Thomas Spencer: Random Banded and Sparse Matrices

III Applications of Random Matrix Theory

24: Jon Keating & Nina Snaith: Number Theory

25: Grigori Olshanski: Random Permutations

26: Jeremie Bouttier: Enumeration of Maps

27: Poul Zinn-Justin & Jean-Bernard Zuber: Knot Theory

28: Noureddine El Karoui: Multivariate Statistics

29: Leonid Chekhov: Algrebraic Geometry

30: Ian Kostov: Two-Dimensional Quantum Gravity

31: Marcos Marin~o: String Theory

32: Jac Verbaarschot: Quantum Chromodynamics

33: Sebastian Mu"ller & Martin Sieber: Quantum Chaos and Quantum Graphs

34: Yan Fyodorov & Dmitry Savin: Resonance Scattering in Chaotic Systems

35: Carlo W. J. Beenakker: Condensed Matter Physics

36: Carlo W. J. Beenakker: Optics

37: Satya N. Majumdar: Extreme Eigenvalues of Wishart Matrices and Entangled Bipartite System

38: Patrik L. Ferrari & Herbert Spohn: Random Growth Models

39: Anton Zabrodin: Laplacian Growth

40: Jean-Phillipe Bouchard & Marc Potters: Financial Applications

41: Antonia Tulino & Sergio Verdu': Information Theory

42: Graziano Vernizzi & Henri Orland: Ribonucleic Acid Folding

43: Geoff Rodgers & Taro Nagao: Complex Networks