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Large Deviations and the Lukic Conjecture

Breuer, Jonathan and Simon, Barry and Zeitouni, Ofer (2018) Large Deviations and the Lukic Conjecture. Duke Mathematical Journal, 167 (15). pp. 2857-2902. ISSN 0012-7094.

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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.

Item Type:Article
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URLURL TypeDescription Paper Paper
Simon, Barry0000-0003-2561-8539
Alternate Title:Large Deviations and Sum Rules for Spectral Theory - A Pedagogical Approach
Additional Information:© 2018 Duke University Press. Received: 15 March 2017; Revised: 16 May 2018; First published online 3 October 2018. We thank Peter Yuditskii for telling two of us about [8] and Fabrice Gamboa, Jan Nagel, and Alain Rouault for useful discussions. Breuer’s work was partially supported by Israel Science Foundation grant 399/16 and by United States–Israel Binational Science Foundation grant 2014337. Simon’s work was partially supported by National Science Foundation grant DMS-1265592 and by United States–Israel Binational Science Foundation grant 2014337. Zeitouni’s work was partially supported by a grant from the Israel Science Foundation.
Funding AgencyGrant Number
Israel Science Foundation399/16
Binational Science Foundation (USA-Israel)2014337
Subject Keywords:sum rules, large deviations, orthogonal polynomials
Classification Code:2010 Mathematics Subject Classification. Primary 60F10; Secondary 35P05, 42C05
Record Number:CaltechAUTHORS:20170509-082734416
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Official Citation:Breuer, Jonathan; Simon, Barry; Zeitouni, Ofer. Large deviations and the Lukic conjecture. Duke Math. J. 167 (2018), no. 15, 2857-2902. doi:10.1215/00127094-2018-0027.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77289
Deposited By: Ruth Sustaita
Deposited On:09 May 2017 21:44
Last Modified:01 Nov 2018 17:30

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