Stability of Asymptotics of Christoffel–Darboux Kernels

Abstract

We study the stability of convergence of the Christoffel–Darboux kernel, associated with a compactly supported measure, to the sine kernel, under perturbations of the Jacobi coefficients of the measure. We prove stability under variations of the boundary conditions and stability in a weak sense under ℓ^(1) and random ℓ^(2) diagonal perturbations. We also show that convergence to the sine kernel at x implies that μ({x}) = 0.

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