Large Deviations and Sum Rules for Spectral Theory - A Pedagogical Approach

Abstract

This is a pedagogical exposition of the large deviation approach to sum rules pioneered by Gamboa, Nagel and Rouault. We'll explain how to use their ideas to recover the Szeg}o and Killip{ Simon Theorems. The primary audience is spectral theorists and people working on orthogonal polynomials who have limited familiarity with the theory of large deviations.

New version adds appendix with a detailed proof of the Killip-Nenciu theorem and includes minor corrections