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 Szegő 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.
Bibliographical noteFunding Information:
1 Research supported in part by Israeli BSF Grant No. 2014337. 2 Research supported in part by NSF grant DMS-1265592 and in part by Israeli BSF Grant No. 2014337. 3 Research supported in part by a grant from the Israel Science Foundation.
© European Mathematical Society
- Large deviations
- Orthogonal polynomials
- Sum rules