The Oxford Handbook of Random Matrix Theory

Gernot Akemann, Professor of Mathematical Physics, Department of Physics, Bielefeld University, Germany,Jinho Baik, Associate Professor, Department of Mathematics, University of Michigan,Philippe Di Francesco, Research Engineer, Institut de Physique Theorique du Commissariat a l'Energie Atomique, Saclay

Gernot Akemann gained his PhD in theoretical physics at Leibniz Universitat 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 Universite Pierre et Marie Curie (Paris 6). He completed his habilitation in mathematics in 2004 at the Universite 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.

Forward, Freeman Dyson
I Introduction
1. Guide to the Handbook, Gernot Akenmann, Jinho Baik & Philippe Di Francesco
2. History, Oriol Bohigas & Hans Weidenmuller
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. Painleve 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-Jurgen Sommers
19. Characteristic Polynomials, Edouard Brezin & Sinobu Hikami
20. Beta Ensembles, Peter Forrester
21. Wigner Matrices, Gerard 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 Marino
32. Quantum Chromodynamics, Jac Verbaarschot
33. Quantum Chaos and Quantum Graphs, Sebastian Muller & 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 Verdu
42. Ribonucleic Acid Folding, Graziano Vernizzi & Henri Orland
43. Complex Networks, Geoff Rodgers & Taro Nagao