Large deviations and the Lukic conjecture

Jonathan Breuer, Barry Simon, Ofer Zeitouni

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageAmerican English
Pages (from-to)2857-2902
Number of pages46
JournalDuke Mathematical Journal
Volume167
Issue number15
DOIs
StatePublished - 1 Oct 2018

Bibliographical note

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© 2018.

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