Random matrix models and their applications
著者
書誌事項
Random matrix models and their applications
（Mathematical Sciences Research Institute publications, 40）
Cambridge University Press, 2011, c2001
- : pbk
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注記
"First published 2001" -- T.p. verso
"First paperback edition 2011" -- T.p. verso
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
- 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.
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