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 ${\ell }^1$ and random ${\ell }^2$ diagonal perturbations. We also show that convergence to the sine kernel at $x$ implies that $\mu (\{x\})=0$.

References in corpus (2)

• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators
• Bulk Universality and Clock Spacing of Zeros for Ergodic Jacobi Matrices with A.C. Spectrum

Cited by in corpus (4)

• Universality of mesoscopic fluctuations for orthogonal polynomial ensembles
• An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles
• Discrete self-adjoint Dirac systems: asymptotic relations, Weyl functions and Toeplitz matrices
• An approach to universality using Weyl m-functions