The Oxford Handbook of Random Matrix Theory

Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco

Oxford Handbooks

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

The Oxford Handbook of Random Matrix Theory

Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco

Description

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.

The Oxford Handbook of Random Matrix Theory

Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco

Oxford Handbooks

Forward, Freeman Dyson
I Introduction
1:Guide to the Handbook, Gernot Akenmann, Jinho Baik & Philippe Di Francesco
2:History, Oriol Bohigas & Hans Weidenmüller
II Properties of Random Matrix Theory
3:Symmetry Classes, Martin Zirnbauer
4:Spectral Statisitics of Unitary Emsembles, Greg W. Anderson
5:Spectral Statistics of Orthogonal and Symplectic Ensembles, Mark Adler
6:Universality, Arno Kuijlaars
7:Supersymmetry, Thomas Guhr
8:Replica Approach, Eugene Kanzieper
9:Painlevé Transcendents, Alexander Its
10:Random Matrices and Integrable Systems, Pierre van Moerbeke
11:Determinantal Point Processes, Alexei Borodin
12:Random Matrix Representations of Critical Statistics, Vladimir Kravtsov
13:Heavy-Tailed Random Matrices, Zdzislaw Burda & Jerzy Jurkiewicz
14:Phase Transitions, Giovanni Cicuta & Luca Molinari
15:Two-Matrix Models and Biorthogonal Polynomials, Marco Bertola
16:Loop Equation Method, Nicolas Orantin
17:Unitary Integrals and Related Matrix Models, Alexei Morozov
18:Non-Hermitian Ensembles, Boris Khoruzhenko & Hans-Jürgen Sommers
19:Characteristic Polynomials, Edouard Brézin & Sinobu Hikami
20:Beta Ensembles, Peter Forrester
21:Wigner Matrices, Gérard Ben Arous & Guionnet
22:Free Probability Theory, Roland Speicher
23:Random Banded and Sparse Matrices, Thomas Spencer
III Applications of Random Matrix Theory
24:Number Theory, Jon Keating & Nina Snaith
25:Random Permutations, Grigori Olshanski
26:Enumeration of Maps, Jeremie Bouttier
27:Knot Theory, Poul Zinn-Justin & Jean-Bernard Zuber
28:Multivariate Statistics, Noureddine El Karoui
29:Algrebraic Geometry, Leonid Chekhov
30:Two-Dimensional Quantum Gravity, Ian Kostov
31:String Theory, Marcos Mariño
32:Quantum Chromodynamics, Jac Verbaarschot
33:Quantum Chaos and Quantum Graphs, Sebastian Müller & Martin Sieber
34:Resonance Scattering in Chaotic Systems, Yan Fyodorov & Dmitry Savin
35:Condensed Matter Physics, Carlo W. J. Beenakker
36:Optics, Carlo W. J. Beenakker
37:Extreme Eigenvalues of Wishart Matrices and Entangled Bipartite System, Satya N. Majumdar
38:Random Growth Models, Patrik L. Ferrari & Herbert Spohn
39:Laplacian Growth, Anton Zabrodin
40:Financial Applications, Jean-Phillipe Bouchard & Marc Potters
41:Information Theory, Antonia Tulino & Sergio Verdú
42:Ribonucleic Acid Folding, Graziano Vernizzi & Henri Orland
43:Complex Networks, Geoff Rodgers & Taro Nagao

The Oxford Handbook of Random Matrix Theory

Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco

Oxford Handbooks

Author Information

Edited by Gernot Akemann, Professor of Mathematical Physics, Department of Physics, Bielefeld University, Germany, Jinho Baik, Associate Professor, Department of Mathematics, University of Michigan, and Philippe Di Francesco, Research Engineer, Institut de Physique Théorique du Commissariat à l'Énergie Atomique, Saclay

Gernot Akemann gained his PhD in theoretical physics at Leibniz Universität Hannover in 1996. He was an EU Marie-Curie Fellow from 1996 until 1998. He has worked at MPIK Heidelberg and later at CEA SPhT, where he held a Heisenberg fellowship. He is currently Professor for Mathematical Physics at the Faculty of Physics, Bielefeld University, Germany.

Jinho Baik gained his PhD in mathematics at New York University in 1999. He has been the recipient of the AMS Centennial Fellowship, the Sloan Research Fellowship and he won the CMFT2005 Young Researcher Award. He is currently an associate professor in the Department of Mathematics, University of Michigan.

Philippe Di Francesco gained his PhD in theoretical physics in 1989 at the Université Pierre et Marie Curie (Paris 6). He completed his habilitation in mathematics in 2004 at the Université Paris Diderot (Paris 7). He was a postdoctoral researcher in the Department of Mathematics, Princeton and a professor with the Department of Mathematics, University of North Carolina. He has been a research member of IPHT, CEA Saclay since 1989.

Contributors:

Gernot Akemann (Bielefeld University), Jinho Baik (University of Michigan) & Philippe Di Francesco (Institut de Physique Théorique du Commissariat à l'Énergie Atomique)
Oriol Bohigas (Université Paris-Sud) & Hans Weidenmüller (Max-Planck-Institut für Kernphysik)
Jean-Bernard Zirnbauer (Cologne University)
Greg W. Anderson (University of Minnesota)
Mark Adler (Brandeis University)
Arno Kuijlaars (Katholieke Universiteit Leuven)
Thomas Guhr (Universität Duisburg-Essen)
Eugene Kanzieper (Holon Institute of Technology)
Alexander Its (Indiana University)
Pierre van Moerbeke (Université Catholique de Louvain)
Alexei Borodin (California Institute of Technology)
Vladimir Kravtsov (The Abdus Salam International Centre for Theoretical Physics)
Zdzislaw Burda (Jagiellonian University) & Jerzy Jurkiewicz (Jagiellonian University)
Giovanni Cicuta (Università degli studi di Parma) & Luca Molinari (Università di Milano)
Marco Bertola (Concordia University)
Nicolas Orantin (CERN)
Alexei Morozov (Institute of Theoretical and Experimental Physics, Moscow)
Boris Khoruzhenko (Queen Mary University of London) & Sommers (Universität Duisburg-Essen)
Edouard Brézin (Laboratoire de Physique Théorique de l'Ecole Normale Supérieure) & Hikami (University of Tokyo)
Peter Forrester (University of Melbourne)
Gérard Ben Arous (New York University) & Guionnet (École Normale Supérieure)
Roland Speicher (Queen's University, Canada)
Thomas Spencer (Institute for Advanced Studies, Princeton)