Large Deviations and the Lukic Conjecture

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 paper provides support for the idea that Lukic's replacement for Simon's conjecture might be true.

Version 2 has minor changes and is the version submitted to a journal. Version 3 has minor changes and incorporates referees' comments

References in corpus (2)

• On generalized sum rules for Jacobi matrices
• An Algebra Model for the Higher Order Sum Rules

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• An Algebra Model for the Higher Order Sum Rules
• Sum rules and large deviations for spectral matrix measures in the Jacobi ensemble
• Sum rules and large deviations for spectral measures on the unit circle
• On some gateways between sum rules