**Contemporary Mathematics**

Volume: 458;
2008;
420 pp;
Softcover

MSC: Primary 15; 35; 37; 42; 60;

Print ISBN: 978-0-8218-4240-9

Product Code: CONM/458

List Price: $112.00

AMS Member Price: $89.60

MAA member Price: $100.80

**Electronic ISBN: 978-0-8218-8137-8
Product Code: CONM/458.E**

List Price: $112.00

AMS Member Price: $89.60

MAA member Price: $100.80

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# Integrable Systems and Random Matrices: In Honor of Percy Deift

Share this page *Edited by *
*Jinho Baik; Thomas Kriecherbauer; Luen-Chau Li; Kenneth D. T-R McLaughlin; Carlos Tomei*

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

## Integrable Systems and Random Matrices: In Honor of Percy Deift

- Contents vii8 free
- Preface ix10 free
- List of Participants xi12 free
- Percy Deift at integer times 116 free
- Birkhoff normal form for the periodic Toda lattice 1126
- Asymptotics of a Class of Operator Determinants with Application to the Cylindrical Toda Equations 3146
- Connection formulas for the third Painlevé transcendent in the complex plane 5570
- Nonlinear Fourier Transforms and Integrability in Multidimensions 7186
- Numerical study of a multiscale expansion of Korteweg-de Vries and Camassa-Holm equation 8196
- Long-time asymptotics of the Camassa-Holm equation on the line 99114
- Semiclassical Focusing Nonlinear Schrödinger equation in the pure radiation case: Riemann-Hilbert Problem approach 117132
- From Stationary Phase to Steepest Descent 145160
- Riemann-Hilbert Problems with Lots of Discrete Spectrum 163178
- Locating the zeros of partial sums of ez with Riemann-Hilbert methods 183198
- Two variable Deformations of the Chebyshev measure 197212
- Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump 215230
- Orthogonal Polynomials, Jacobi Matrices and Random Matrices 249264
- Universality in unitary random matrix ensembles when the soft edge meets the hard edge 265280
- A new approach to universality limits at the edge of the spectrum 281296
- On the gap probability generating function at the spectrum edge in the case of orthogonal symmetry 291306
- An interpolation between Airy and Pearcey processes 303318
- The universal Airy1 and Airy2 processes in the Totally Asymmetric Simple Exclusion Process 321336
- On some special directed last-passage percolation models 333348
- Discrete spacetime and its applications 347362
- The Arctic Circle Revisited 361376
- Moduli of continuity and average decay of Fourier transforms: two-sided estimates 377392
- Eigenvalues of Schrödinger Operators in Gaps of the Essential Spectrum — an Overview 393408
- Transition Measures for the Stochastic Burgers Equation 409424
- Some open problems in random matrix theory and the theory of integrable systems 419434