Integrable Systems and Random Matrices

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.

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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Integrable Systems and Random Matrices

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