Duke Mathematical Journal
- Duke Math. J.
- Volume 167, Number 15 (2018), 2857-2902.
Large deviations and the Lukic conjecture
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.
Duke Math. J., Volume 167, Number 15 (2018), 2857-2902.
Received: 15 March 2017
Revised: 16 May 2018
First available in Project Euclid: 3 October 2018
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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. https://projecteuclid.org/euclid.dmj/1538532052