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

Jonathan Breuer, Barry Simon, Ofer Zeitouni

Type: Article

Publication Date: 2018-10-22

Citations: 14

DOI: https://doi.org/10.4171/jst/235

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.

Locations

Journal of Spectral Theory - View
arXiv (Cornell University) - View - PDF
CaltechAUTHORS (California Institute of Technology) - View - PDF

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Works Cited by This (29)

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+	Representations of Finite and Compact Groups	1995	Barry Simon
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+	On the 1/n Expansion for Some Unitary Invariant Ensembles of Random Matrices	2001	Sergio Albeverio L. А. Pastur Mariya Shcherbina
+	A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices	2004	Barry Simon
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+	Aging of spherical spin glasses	2001	Gérard Ben Arous Amir Dembo Alice Guionnet
+	Orthogonal polynomials from the viewpoint of scattering theory	1974	K. M. Case
+	Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory	1999	Percy Deift T. Kriecherbauer K. T-R McLaughlin Stephanos Venakides Xin Zhou