English

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

Probability 2016-12-02 v2

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.

Cite

@article{arxiv.1608.01467,
  title  = {Large Deviations and Sum Rules for Spectral Theory - A Pedagogical Approach},
  author = {Jonathan Breuer and Barry Simon and Ofer Zeitouni},
  journal= {arXiv preprint arXiv:1608.01467},
  year   = {2016}
}

Comments

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

R2 v1 2026-06-22T15:12:02.374Z