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Large deviations and sum rules for spectral theory: a pedagogical approach
Jonathan Breuera, Barry Simon Ab, Ofer Zeitounic
- aHebrew University, Jerusalem, Israel
- bCaltech, Pasadena, USA
- cWeizmann Institute of Science, Rehovot, Israel and Courant Institute of Mathematical Sciences, New York, USA
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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 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.