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Product Code:  CONM/458.E 
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Book DetailsContemporary MathematicsVolume: 458; 2008; 420 ppMSC: 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 wideranging 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.
ReadershipGraduate 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 Kortewegde Vries and CamassaHolm equation [ MR 2411902 ]

Anne Boutet de Monvel and Dmitry Shepelsky  Longtime asymptotics of the CamassaHolm equation on the line [ MR 2411903 ]

Alexander Tovbis, Stephanos Venakides and Xin Zhou  Semiclassical focusing nonlinear Schrödinger equation in the pure radiation case: RiemannHilbert problem approach [ MR 2411904 ]

Spyridon Kamvissis  From stationary phase to steepest descent [ MR 2411905 ]

Peter D. Miller  RiemannHilbert 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 RiemannHilbert 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 lastpassage 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: twosided 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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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 wideranging 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.
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 Kortewegde Vries and CamassaHolm equation [ MR 2411902 ]

Anne Boutet de Monvel and Dmitry Shepelsky  Longtime asymptotics of the CamassaHolm equation on the line [ MR 2411903 ]

Alexander Tovbis, Stephanos Venakides and Xin Zhou  Semiclassical focusing nonlinear Schrödinger equation in the pure radiation case: RiemannHilbert problem approach [ MR 2411904 ]

Spyridon Kamvissis  From stationary phase to steepest descent [ MR 2411905 ]

Peter D. Miller  RiemannHilbert 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 RiemannHilbert 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 lastpassage 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: twosided 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 ]