# Random Matrix Theory, Interacting Particle Systems, and Integrable Systems (Mathematical Sciences Research Institute Publications)

Cambridge University Press, 12/15/2014

EAN 9781107079922, ISBN10: 1107079926

Hardcover, 540 pages, 23.4 x 15.6 x 3 cm

Language: English

Random matrix theory is at the intersection of linear algebra, probability theory and integrable systems, and has a wide range of applications in physics, engineering, multivariate statistics and beyond. This volume is based on a Fall 2010 MSRI program which generated the solution of long-standing questions on universalities of Wigner matrices and beta-ensembles and opened new research directions especially in relation to the KPZ universality class of interacting particle systems and low-rank perturbations. The book contains review articles and research contributions on all these topics, in addition to other core aspects of random matrix theory such as integrability and free probability theory. It will give both established and new researchers insights into the most recent advances in the field and the connections among many subfields.

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. RiemannÃ¢â‚¬â€œHilbert 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 KortewegÃ¢â‚¬â€œde 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 Ãâ€ž-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 KardarÃ¢â‚¬â€œParisiÃ¢â‚¬â€œZhang 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 ÃŽÂ² 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 TracyÃ¢â‚¬â€œWidom 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.