Integrable Systems and Random Matrices

by Baik, Jinho; Kriecherbauer, Thomas; Li, Luen-Chau; McLaughlin, Kenneth T-R; Tomei, Carlos

• ISBN13: 9780821842409
• ISBN10: 0821842404
• Format: Paperback
• Copyright: 2008-06-19
• Publisher: Amer Mathematical Society

Summary

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 associatedwith 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 totechniques 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.

Table of Contents

Percy Deift at integer times

Birkhoff normal form for the periodic toda lattice

Asymptotics of a class of operator determinants with application to the cylindrical toda equations

Connection formulas for the third Painleve transcendent in the complex plane

Nonlinear Fourier transforms and integrability in multidimensions

Numerical study of a multiscale expansion of Korteweg-de Vries and Camassa-Holm equation

Long-time asymptotics of the Camassa-Holm equation on the line

Semiclassical focusing nonlinear Schrodinger equation in the pure radiation case: Riemann-Hilbert problem approach

From stationary phase to steepest descent

Riemann-Hilbert problems with lots of discrete spectrum

Locating the zeros of partial sums of $e^z$ with Riemann-Hilbert methods

Two variable deformations of the Chebyshev measure

Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump

Orthogonal polynomials, Jacobi matrices and random matrices

Universality in unitary random matrix ensembles when the soft edge meets the hard edge

A new approach to universality limits at the edge of the spectrum

On the gap probability generating function at the spectrum edge in the case of orthogonal symmetry

An interpolation between Airy and Pearcey processes

The universal Airy$_1$ and Airy$_2$ processes in the toally asymmetric simple exclusion process

On some special directed last-passage percolation models

Discrete spacetime and its applications

The arctic circle revisited

Moduli of continuity and average decay of Fourier transforms: Two-sided estimates

Eigenvalues of Schrodinger operators in gaps of the essential spectrum–An overview

Transition measures for the stochastic Burgers equation

Some open problems in random matrix theory and the theory of integrable systems

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