Información General

• Autores: Pavel M. Bleher (coord.), Alexander Its (coord.)
• Editores: Cambridge University Press
• Año de publicación: 2001
• Colecciones: Mathematical Sciences Research Institute publications, 40
• País: Estados Unidos
• Idioma: inglés
• ISBN: 0-521-80209-1
• Texto completo no disponible (Saber más ...)

Resumen

• 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.

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Listado de artículos

• • Symmetrized Random Permutations

    Jinho Baik, Eric M. Rains

    págs. 1-19

    

  • Hankel Determinants as Fredholm Determinants

    Estelle L. Basor, Yang Chen, Harold Widom

    págs. 21-29

    

  • Universality and Scaling of Zeros on Symplectic Manifolds

    Pavel M. Bleher, Bernard Shiffman, Steve Zelditch

    págs. 31-69

    

  • Z-Measures on Partitions, Robinson-Schensted-Knuth Correspondence, and beta=2 Random Matrix Ensembles

    Alexei Borodin, Grigori Olshanski

    págs. 71-94

    

  • Phase Transitions and Random Matrices

    Giovanni M. Cicuta

    págs. 95-109

    

  • Matrix Model Combinatorics: applications to Folding and Coloring

    Philippe Di Francesco

    págs. 111-170

    

  • Interrelationships Between Orthogonal, Unitary and Symplectic Matrix Ensembles

    Peter J. Forrester, Eric M. Rains

    págs. 171-207

    

  • Dual Isomonodromic Tau Functions and Determinants of Integrable Fredholm Operators

    John Harnad

    págs. 209-224

    

  • Orthogonal Polynomials and Random Matrix Theory

    Mourad E. H. Ismail

    págs. 225-244

    

  • Random Words, Toeplitz Determinants and Integrable Systems, I

    Alexander Its, Craig A. Tracy, Harold Widom

    págs. 245-258

    

  • Random permutations and the discrete Bessel kernel

    Kurt Johansson

    págs. 259-269

    

  • Solvable Matrix Models

    Vladimir Kazakov

    págs. 271-283

    

  • Tau-function for Analytic Curves

    I.K. Kostov, Igor Krichever, M. Mineev-Weinstein, P.B. Wiegmann, A. Zabrodin

    págs. 285-299

    

  • Integration over Angular Variables for Two Coupled Matrices

    G. Mahoux, M.L. Mehta, J.M. Normand

    págs. 301-320

    

  • Integrable lattices: random matrices and random permutations

    Pierre van Moerbeke

    págs. 321-406

    

  • SL(2) and z-measures

    Andrei Okounkov

    págs. 407-420

    

  • Some Matrix Integrals related to knots and Links

    Paul Zinn Justin

    págs. 421-438