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Journal of Spectral Theory


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Volume 8, Issue 4, 2018, pp. 1551–1581
DOI: 10.4171/JST/235

Published online: 2018-10-22

Large deviations and sum rules for spectral theory: a pedagogical approach

Jonathan Breuer[1], Barry Simon[2] and Ofer Zeitouni[3]

(1) Hebrew University, Jerusalem, Israel
(2) Caltech, Pasadena, USA
(3) Weizmann Institute of Science, Rehovot, Israel and Courant Institute of Mathematical Sciences, New York, USA

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.

Keywords: Sum rules, large deviations, orthogonal polynomials

Breuer Jonathan, Simon Barry, Zeitouni Ofer: Large deviations and sum rules for spectral theory: a pedagogical approach. J. Spectr. Theory 8 (2018), 1551-1581. doi: 10.4171/JST/235