An approach to universality using Weyl m-functions
Benjamin Eichinger,
Milivoje Lukić,
Brian Simanek
Abstract:We describe an approach to universality limits for orthogonal polynomials on the real line which is completely local and uses only the boundary behavior of the Weyl m-function at the point. We show that bulk universality of the Christoffel-Darboux kernel holds for any point where the imaginary part of the m-function has a positive finite nontangential limit. This approach is based on studying a matrix version of the Christoffel-Darboux kernel and the realization that bulk universality for this kernel at a poin… Show more
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