Large deviations for some random matrix models and a conjecture

Atelier
« Asymptotiques des systèmes intégrables, matrices aléatoires et processus aléatoires, et universalité.
Un hommage à l’occasion du e anniversaire de Percy Deift »
– juin 
Workshop
“Asymptotics in integrable systems, random matrices and random processes and universality:
In honour of Percy Deift’s th birthday”
June –, 
Large deviations for some random matrix models and
a conjecture of Lukic
Barry Simon*
[email protected]
I will first give a quick history of the use of sum rules in spectral theory focusing on a conjecture of Lukic. I’ll then make propaganda for a method of Gamboa, Nagel and Rouault
(http://arxiv.org/abs/1407.1384v1) using large deviations on matrix models to generate positive sum rules. Finally I’ll discuss work in progress by Breuer, Simon and Zeitouni
applying this method to OPUC with singularities at finitely many points.
* Department
of Mathematics, Caltech, Pasadena, CA 91125, USA.