Large deviations for some random matrix models and a conjecture
Transcription
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.