Irina Nenciu : Matrix models for beta-ensembles

Posted by , part of the Graduate Student Colloquium.

At

Oct. 30, 2009, 3 p.m.

In

SEO 636

Abstract

In this talk, I will give a brief overview of both classical and modern ideas related to random matrix theory, with emphasis on beta-ensembles for general beta positive. These random matrices have eigenvalues following the Gibbs distribution for n particles of the Coulomb gas on the unit circle or the real line, at inverse temperature beta. In particular, I will highlight the change of perspective, from the classical unitary ensembles, which incorporate a lot of symmetry, to these new ensembles, which are very sparse, and some of the methods we use in our construction, inspired by orthogonal polynomial theory. Finally, I will present some of the consequences of these constructions, for example their relation to stochastic PDEs.