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arXiv · 1302.7237

Stability of Asymptotics of Christoffel-Darboux Kernels

Jonathan Breuer·Yoram Last·Barry Simon
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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 $\ell^1$ and random $\ell^2$ diagonal perturbations. We also show that convergence to the sine kernel at $x$ implies that $μ(\{x\})=0$.

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BibTeXRIS

Jonathan Breuer, Yoram Last, Barry Simon. 2013-02-28. Stability of Asymptotics of Christoffel-Darboux Kernels. https://doi.org/10.1007/s00220-014-1913-4

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