# Mathematical Sciences Research Institute

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# MSRI Publications – Volume 65

## Random Matrix Theory, Interacting Particle Systems and Integrable Systems

### Edited by Percy Deift and Peter Forrester Contents

Front matter (front page, copyright page)
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Table of contents
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Preface by Percy Deift and Peter Forrester, ix–x
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Universality conjecture for all Airy, sine and Bessel kernels in the complex plane, by Gernot Akemann and Michael J. Phillips, 1–23
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On a relationship between high rank cases and rank one cases of Hermitian random matrix models with external source, by Jinho Baik and Dong Wang, 25–38
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Riemann–Hilbert approach to the six-vertex model, by Pavel Bleher and Karl Liechty, 39–56
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CLT for spectra of submatrices of Wigner random matrices, II: Stochastic evolution, by Alexei Borodin, 57–69
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Critical asymptotic behavior for the Korteweg–de Vries equation and in random matrix theory, by Tom Claeys and Tamara Grava, 71–92
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On the asymptotics of a Toeplitz determinant with singularities, by Percy Deift, Alexander Its, and Igor Krasovsky, 93–146
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Asymptotic analysis of the two-matrix model with a quartic potential, by Maurice Duits, Arno B. J. Kuijlaars, Man Yue Mo, 147–161
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Conservation laws of random matrix theory, by Nicholas M. Ercolani, 163–197
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Asymptotics of spacing distributions 50 years later, by Peter Forrester, 199–222
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Applications of random matrix theory for sensor array imaging with measurement noise, by Josselin Garnier and Knut Sølna, 223–245
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Convolution symmetries of integrable hierarchies, matrix models and $\tau$-functions, by John Harnad and Alexander Yu. Orlov, 247–275
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Universality limits via "old style" analysis, by Doron S. Lubinsky, 277–292
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Fluctuations and large deviations of some perturbed random matrices, by Mylène Maïda, 293–307
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Three lectures on free probability, by Jonathan Novak, 309–383
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Whittaker functions and related stochastic processes, by Neil O'Connell, 385–409
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How long does it take to compute the eigenvalues of a random symmetric matrix?, by Christian W. Pfrang, Percy Deift, and Govind Menon, 411–442
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Exact solutions of the Kardar–Parisi–Zhang equation and weak universality for directed random polymers, by Jeremy Quastel, 443–450
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Replica analysis of the one-dimensional KPZ equation, by Tomohiro Sasamoto, 451–462
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Asymptotic expansions for $\beta$ matrix models and their applications to the universality conjecture, by Mariya Shcherbina, 463–482
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KPZ scaling theory and the semidiscrete directed polymer model, by Herbert Spohn, 483–493
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Experimental realization of Tracy–Widom distributions and beyond: KPZ interfaces in turbulent liquid crystal, by Kazumasa A. Takeuchi, 495–507
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Random matrices: the four-moment theorem for Wigner ensembles, by Terence Tao and Van Vu, 509–528
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