Random Matrix Theory, Interacting Particle Systems, and Integrable Systems [Hardcover]

This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.This volume, based on the Fall 2010 MSRI program, includes review articles, research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles, and other core aspects of random matrix theory such as integrability and free probability theory.This volume, based on the Fall 2010 MSRI program, includes review articles, research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles, and other core aspects of random matrix theory such as integrability and free probability theory.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. RiemannHilbert approach to the six-vertex model Pavel Bleher and Karl Liechty; 4. CLT for spectra of submatrices of Wigner random matrices, II: stochastic evolutionlÓ)