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Integrable Systems and Random Matrices: In Honor of Percy Deift
 
Edited by: Jinho Baik University of Michigan, Ann Arbor, MI
Thomas Kriecherbauer Ruhr-Universität Bochum, Bochum, Germany
Luen-Chau Li Pennsylvania State University, University Park, PA
Kenneth D. T-R McLaughlin University of Arizona, Tucson, AZ
Carlos Tomei PUC - Rio de Janeiro, Rio de Janeiro, Brazil
Front Cover for Integrable Systems and Random Matrices
Available Formats:
Electronic ISBN: 978-0-8218-8137-8
Product Code: CONM/458.E
List Price: $112.00
MAA Member Price: $100.80
AMS Member Price: $89.60
Front Cover for Integrable Systems and Random Matrices
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  • Front Cover for Integrable Systems and Random Matrices
  • Back Cover for Integrable Systems and Random Matrices
Integrable Systems and Random Matrices: In Honor of Percy Deift
Edited by: Jinho Baik University of Michigan, Ann Arbor, MI
Thomas Kriecherbauer Ruhr-Universität Bochum, Bochum, Germany
Luen-Chau Li Pennsylvania State University, University Park, PA
Kenneth D. T-R McLaughlin University of Arizona, Tucson, AZ
Carlos Tomei PUC - Rio de Janeiro, Rio de Janeiro, Brazil
Available Formats:
Electronic ISBN:  978-0-8218-8137-8
Product Code:  CONM/458.E
List Price: $112.00
MAA Member Price: $100.80
AMS Member Price: $89.60
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 4582008; 420 pp
    MSC: Primary 15; 35; 37; 42; 60;

    This volume contains the proceedings of a conference held at the Courant Institute in 2006 to celebrate the 60th birthday of Percy A. Deift. The program reflected the wide-ranging contributions of Professor Deift to analysis with emphasis on recent developments in Random Matrix Theory and integrable systems. The articles in this volume present a broad view on the state of the art in these fields. Topics on random matrices include the distributions and stochastic processes associated with local eigenvalue statistics, as well as their appearance in combinatorial models such as TASEP, last passage percolation and tilings. The contributions in integrable systems mostly deal with focusing NLS, the Camassa–Holm equation and the Toda lattice. A number of papers are devoted to techniques that are used in both fields. These techniques are related to orthogonal polynomials, operator determinants, special functions, Riemann–Hilbert problems, direct and inverse spectral theory. Of special interest is the article of Percy Deift in which he discusses some open problems of Random Matrix Theory and the theory of integrable systems.

    Readership

    Graduate students and research mathematicians interested in random matrix theory or integrable systems.

  • Table of Contents
     
     
    • Articles
    • Carlos Tomei - Percy Deift at integer times [ MR 2411897 ]
    • Andreas Henrici and Thomas Kappeler - Birkhoff normal form for the periodic Toda lattice [ MR 2411898 ]
    • Harold Widom - Asymptotics of a class of operator determinants with application to the cylindrical Toda equations [ MR 2411899 ]
    • V. Yu. Novokshenov - Connection formulas for the third Painlevé transcendent in the complex plane [ MR 2411900 ]
    • A. S. Fokas - Nonlinear Fourier transforms and integrability in multidimensions [ MR 2411901 ]
    • Tamara Grava and Christian Klein - Numerical study of a multiscale expansion of Korteweg-de Vries and Camassa-Holm equation [ MR 2411902 ]
    • Anne Boutet de Monvel and Dmitry Shepelsky - Long-time asymptotics of the Camassa-Holm equation on the line [ MR 2411903 ]
    • Alexander Tovbis, Stephanos Venakides and Xin Zhou - Semiclassical focusing nonlinear Schrödinger equation in the pure radiation case: Riemann-Hilbert problem approach [ MR 2411904 ]
    • Spyridon Kamvissis - From stationary phase to steepest descent [ MR 2411905 ]
    • Peter D. Miller - Riemann-Hilbert problems with lots of discrete spectrum [ MR 2411906 ]
    • T. Kriecherbauer, A. B. J. Kuijlaars, K. D. T.-R. McLaughlin and P. D. Miller - Locating the zeros of partial sums of $e^z$ with Riemann-Hilbert methods [ MR 2411907 ]
    • Jeffrey S. Geronimo and Plamen Iliev - Two variable deformations of the Chebyshev measure [ MR 2411908 ]
    • A. Its and I. Krasovsky - Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump [ MR 2411909 ]
    • L. Pastur - Orthogonal polynomials, Jacobi matrices and random matrices [ MR 2411910 ]
    • Tom Claeys and Arno B. J. Kuijlaars - Universality in unitary random matrix ensembles when the soft edge meets the hard edge [ MR 2411911 ]
    • D. S. Lubinsky - A new approach to universality limits at the edge of the spectrum [ MR 2411912 ]
    • P. J. Forrester - On the gap probability generating function at the spectrum edge in the case of orthogonal symmetry [ MR 2411913 ]
    • Mark Adler and Pierre van Moerbeke - An interpolation between Airy and Pearcey processes [ MR 2411914 ]
    • Patrik L. Ferrari - The universal ${\rm Airy}_1$ and ${\rm Airy}_2$ processes in the totally asymmetric simple exclusion process [ MR 2411915 ]
    • Kurt Johansson - On some special directed last-passage percolation models [ MR 2411916 ]
    • Eitan Bachmat - Discrete spacetime and its applications [ MR 2411917 ]
    • F. Colomo and A. G. Pronko - The Arctic Circle revisited [ MR 2411918 ]
    • Dimitri Gioev - Moduli of continuity and average decay of Fourier transforms: two-sided estimates [ MR 2411919 ]
    • Rainer Hempel - Eigenvalues of Schrödinger operators in gaps of the essential spectrum—an overview [ MR 2411920 ]
    • Jonathan C. Mattingly and Toufic M. Suidan - Transition measures for the stochastic Burgers equation [ MR 2411921 ]
    • Percy Deift - Some open problems in random matrix theory and the theory of integrable systems [ MR 2411922 ]
  • Additional Material
     
     
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Volume: 4582008; 420 pp
MSC: Primary 15; 35; 37; 42; 60;

This volume contains the proceedings of a conference held at the Courant Institute in 2006 to celebrate the 60th birthday of Percy A. Deift. The program reflected the wide-ranging contributions of Professor Deift to analysis with emphasis on recent developments in Random Matrix Theory and integrable systems. The articles in this volume present a broad view on the state of the art in these fields. Topics on random matrices include the distributions and stochastic processes associated with local eigenvalue statistics, as well as their appearance in combinatorial models such as TASEP, last passage percolation and tilings. The contributions in integrable systems mostly deal with focusing NLS, the Camassa–Holm equation and the Toda lattice. A number of papers are devoted to techniques that are used in both fields. These techniques are related to orthogonal polynomials, operator determinants, special functions, Riemann–Hilbert problems, direct and inverse spectral theory. Of special interest is the article of Percy Deift in which he discusses some open problems of Random Matrix Theory and the theory of integrable systems.

Readership

Graduate students and research mathematicians interested in random matrix theory or integrable systems.

  • Articles
  • Carlos Tomei - Percy Deift at integer times [ MR 2411897 ]
  • Andreas Henrici and Thomas Kappeler - Birkhoff normal form for the periodic Toda lattice [ MR 2411898 ]
  • Harold Widom - Asymptotics of a class of operator determinants with application to the cylindrical Toda equations [ MR 2411899 ]
  • V. Yu. Novokshenov - Connection formulas for the third Painlevé transcendent in the complex plane [ MR 2411900 ]
  • A. S. Fokas - Nonlinear Fourier transforms and integrability in multidimensions [ MR 2411901 ]
  • Tamara Grava and Christian Klein - Numerical study of a multiscale expansion of Korteweg-de Vries and Camassa-Holm equation [ MR 2411902 ]
  • Anne Boutet de Monvel and Dmitry Shepelsky - Long-time asymptotics of the Camassa-Holm equation on the line [ MR 2411903 ]
  • Alexander Tovbis, Stephanos Venakides and Xin Zhou - Semiclassical focusing nonlinear Schrödinger equation in the pure radiation case: Riemann-Hilbert problem approach [ MR 2411904 ]
  • Spyridon Kamvissis - From stationary phase to steepest descent [ MR 2411905 ]
  • Peter D. Miller - Riemann-Hilbert problems with lots of discrete spectrum [ MR 2411906 ]
  • T. Kriecherbauer, A. B. J. Kuijlaars, K. D. T.-R. McLaughlin and P. D. Miller - Locating the zeros of partial sums of $e^z$ with Riemann-Hilbert methods [ MR 2411907 ]
  • Jeffrey S. Geronimo and Plamen Iliev - Two variable deformations of the Chebyshev measure [ MR 2411908 ]
  • A. Its and I. Krasovsky - Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump [ MR 2411909 ]
  • L. Pastur - Orthogonal polynomials, Jacobi matrices and random matrices [ MR 2411910 ]
  • Tom Claeys and Arno B. J. Kuijlaars - Universality in unitary random matrix ensembles when the soft edge meets the hard edge [ MR 2411911 ]
  • D. S. Lubinsky - A new approach to universality limits at the edge of the spectrum [ MR 2411912 ]
  • P. J. Forrester - On the gap probability generating function at the spectrum edge in the case of orthogonal symmetry [ MR 2411913 ]
  • Mark Adler and Pierre van Moerbeke - An interpolation between Airy and Pearcey processes [ MR 2411914 ]
  • Patrik L. Ferrari - The universal ${\rm Airy}_1$ and ${\rm Airy}_2$ processes in the totally asymmetric simple exclusion process [ MR 2411915 ]
  • Kurt Johansson - On some special directed last-passage percolation models [ MR 2411916 ]
  • Eitan Bachmat - Discrete spacetime and its applications [ MR 2411917 ]
  • F. Colomo and A. G. Pronko - The Arctic Circle revisited [ MR 2411918 ]
  • Dimitri Gioev - Moduli of continuity and average decay of Fourier transforms: two-sided estimates [ MR 2411919 ]
  • Rainer Hempel - Eigenvalues of Schrödinger operators in gaps of the essential spectrum—an overview [ MR 2411920 ]
  • Jonathan C. Mattingly and Toufic M. Suidan - Transition measures for the stochastic Burgers equation [ MR 2411921 ]
  • Percy Deift - Some open problems in random matrix theory and the theory of integrable systems [ MR 2411922 ]
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