Random Matrix Models and their Applications

Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.

Pavel Bleher (Edited by), Alexander Its (Edited by)

9780521802093, Cambridge University Press

Hardback, published 4 June 2001

450 pages
23.4 x 15.6 x 2.5 cm, 0.76 kg

Random matrices arise from, and have important applications to, number theory, probability, combinatorics, representation theory, quantum mechanics, solid state physics, quantum field theory, quantum gravity, and many other areas of physics and mathematics. This 2001 volume of surveys and research results, based largely on lectures given at the Spring 1999 MSRI program of the same name, covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems. Its stress on the interaction between physics and mathematics will make it a welcome addition to the shelves of graduate students and researchers in both fields, as will its expository emphasis.

1. Symmetrized random permutations Jinho Baik and Eric M. Rains
2. Hankel determinants as Fredholm determinants Estelle L. Basor, Yang Chen and Harold Widom
3. Universality and scaling of zeros on symplectic manifolds Pavel Bleher, Bernard Shiffman and Steve Zelditch
4. Z measures on partitions, Robinson-Schensted-Knuth correspondence, and random matrix ensembles Alexei Borodin and Grigori Olshanski
5. Phase transitions and random matrices Giovanni M. Cicuta
6. Matrix model combinatorics: applications to folding and coloring Philippe Di Francesco
7. Inter-relationships between orthogonal, unitary and symplectic matrix ensembles Peter J. Forrester and Eric M. Rains
8. A note on random matrices John Harnad
9. Orthogonal polynomials and random matrix theory Mourad E. H. Ismail
10. Random words, Toeplitz determinants and integrable systems I, Alexander R. Its, Craig A. Tracy and Harold Widom
11. Random permutations and the discrete Bessel kernel Kurt Johansson
12. Solvable matrix models Vladimir Kazakov
13. Tau function for analytic Curves I. K. Kostov, I. Krichever, M. Mineev-Vainstein, P. B. Wiegmann and A. Zabrodin
14. Integration over angular variables for two coupled matrices G. Mahoux, M. L. Mehta and J.-M. Normand
15. SL and Z-measures Andrei Okounkov
16. Integrable lattices: random matrices and random permutations Pierre Van Moerbeke
17. Some matrix integrals related to knots and links Paul Zinn-Justin.

Subject Areas: Applied mathematics [PBW], Number theory [PBH], Mathematical foundations [PBC]