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15 October 2018 Large deviations and the Lukic conjecture
Jonathan Breuer, Barry Simon, Ofer Zeitouni
Duke Math. J. 167(15): 2857-2902 (15 October 2018). DOI: 10.1215/00127094-2018-0027

Abstract

We use the large deviation approach to sum rules pioneered by Gamboa, Nagel, and Rouault to prove higher-order sum rules for orthogonal polynomials on the unit circle. In particular, we prove one half of a conjectured sum rule of Lukic in the case of two singular points, one simple and one double. This is important because it is known that the conjecture of Simon fails in exactly this case, so this article provides support for the idea that Lukic’s replacement for Simon’s conjecture might be true.

Citation

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Jonathan Breuer. Barry Simon. Ofer Zeitouni. "Large deviations and the Lukic conjecture." Duke Math. J. 167 (15) 2857 - 2902, 15 October 2018. https://doi.org/10.1215/00127094-2018-0027

Information

Received: 15 March 2017; Revised: 16 May 2018; Published: 15 October 2018
First available in Project Euclid: 3 October 2018

zbMATH: 06982209
MathSciNet: MR3865654
Digital Object Identifier: 10.1215/00127094-2018-0027

Subjects:
Primary: 60F10
Secondary: 35P05 , 42C05

Keywords: large deviations , orthogonal polynomials , sum rules

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 15 • 15 October 2018
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