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Look Inside Random Matrix Models and their Applications

Random Matrix Models and their Applications

Part of Mathematical Sciences Research Institute Publications

Jinho Baik, Eric M. Rains, Estelle L. Basor, Yang Chen, Harold Widom, Pavel Bleher, Bernard Shiffman, Steve Zelditch, Alexei Borodin, Grigori Olshanski, Giovanni M. Cicuta, Philippe Di Francesco, Peter J. Forrester, John Harnad, Mourad E. H. Ismail, Alexander R. Its, Craig A. Tracy, Kurt Johansson, Vladimir Kazakov, I. K. Kostov, I. Krichever, M. Mineev-Vainstein, P. B. Wiegmann, A. Zabrodin, G. Mahoux, M. L. Mehta, J.-M. Normand, Andrei Okounkov, Pierre Van Moerbeke, Paul Zinn-Justin
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  • Date Published: April 2011
  • availability: Available
  • format: Paperback
  • isbn: 9780521175166

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  • 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.

    • Was the first book in this extremely active research area and brings together results that are scattered in physical and mathematical journals
    • Features ideas and approaches developed in both the physics and mathematics communities
    • The contributors are the leading experts in the field
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    Product details

    • Date Published: April 2011
    • format: Paperback
    • isbn: 9780521175166
    • length: 450 pages
    • dimensions: 234 x 156 x 23 mm
    • weight: 0.63kg
    • availability: Available
  • Table of Contents

    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.

  • Editors

    Pavel Bleher, Purdue University, Indiana

    Alexander Its, Purdue University, Indiana

    Contributors

    Jinho Baik, Eric M. Rains, Estelle L. Basor, Yang Chen, Harold Widom, Pavel Bleher, Bernard Shiffman, Steve Zelditch, Alexei Borodin, Grigori Olshanski, Giovanni M. Cicuta, Philippe Di Francesco, Peter J. Forrester, John Harnad, Mourad E. H. Ismail, Alexander R. Its, Craig A. Tracy, Kurt Johansson, Vladimir Kazakov, I. K. Kostov, I. Krichever, M. Mineev-Vainstein, P. B. Wiegmann, A. Zabrodin, G. Mahoux, M. L. Mehta, J.-M. Normand, Andrei Okounkov, Pierre Van Moerbeke, Paul Zinn-Justin

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