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arXiv · 1812.07256

Scaling Limits of Jacobi Matrices and the Christoffel-Darboux Kernel

Jonathan Breuer
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Abstract

We study scaling limits of deterministic Jacobi matrices at a fixed point, $x_0$, and their connection to the scaling limits of the Christoffel-Darboux kernel at that point. We show that in the case that the orthogonal polynomials are bounded at $x_0$, a subsequential limit always exists and can be expressed as a canonical system. We further show that under weak conditions on the associated measure, bulk universality of the CD kernel is equivalent to the existence of a limit of a particular explicit form.

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Jonathan Breuer. 2018-12-18. Scaling Limits of Jacobi Matrices and the Christoffel-Darboux Kernel. https://arxiv.org/abs/1812.07256

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