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

Funding Information:
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 Information:
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.

Publisher Copyright:
© 2018.

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