Random Matrix Theory, Interacting Particle Systems, and Integrable Systems

Percy Deift is a professor at the Courant Institute of Mathematical Sciences, New York University. He is the author of Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach (1999) and was elected to the US National Academy of Sciences in 2009. Peter J. Forrester is a professor in the Department of Mathematics and Statistics at the University of Melbourne, Victoria. He is the author of Log-Gases and Random Matrices (2010) and was elected to the Australian Academy of Science in 2004.

• Preface; 1. Universality conjecture for all Airy, sine and Bessel kernels in the complex plane Gernot Akemann and Michael Phillips; 2. On a relationship between high rank cases and rank one cases of Hermitian random matrix models with external source Jinho Baik and Dong Wang; 3. Riemann–Hilbert approach to the six-vertex model Pavel Bleher and Karl Liechty; 4. CLT for spectra of submatrices of Wigner random matrices, II: stochastic evolution Alexei Borodin; 5. Critical asymptotic behavior for the Korteweg–de Vries equation and in random matrix theory Tom Claeys and Tamara Grava; 6. On the asymptotics of a Toeplitz determinant with singularities Percy Deift, Alexander Its and Igor Krasovsky; 7. Asymptotic analysis of the two-matrix model with a quartic potential Maurice Duits, Arno B. J. Kuijlaars and Man Yue Mo; 8. Conservation laws of random matrix theory Nicholas M. Ercolani; 9. Asymptotics of spacing distributions fifty years later Peter Forrester; 10. Applications of random matrix theory for sensor array imaging with measurement noise Josselin Garnier and Knut Solna; 11. Convolution symmetries of integrable hierarchies, matrix models and τ-functions John Harnad and Alexander Orlov; 12. Universality limits via 'old style' analysis Doron Lubinsky; 13. Fluctuations and large deviations of some perturbed random matrices Mylene Maida; 14. Three lectures on free probability Jonathan Novak; 15. Whittaker functions and related stochastic processes Neil O'Connell; 16. How long does it take to compute the eigenvalues of a random symmetric matrix? Christian Pfrang, Percy Deift and Govind Menon; 17. Exact solutions of the Kardar–Parisi–Zhang equation and weak universality for directed random polymers Jeremy Quastel; 18. Replica analysis of the one-dimensional KPZ equation Tomohiro Sasamoto; 19. Asymptotic expansions for β matrix models and their applications to the universality conjecture Mariya Shcherbina; 20. KPZ scaling theory and the semidiscrete directed polymer model Herbert Spohn; 21. Experimental realization of Tracy–Widom distributions and beyond: KPZ interfaces in turbulent liquid crystal Kazumasa Takeuchi; 22. Random matrices: the four-moment theorem for Wigner ensembles Terence Tao and Van Vu.