Sine kernel asymptotics for a class of singular measures

JOURNAL OF APPROXIMATION THEORY

卷:163

Article

Breuer, Jonathan

关键词: Christoffel-Darboux kernel;    Universality;    Singular continuous measure;   

DOI  :  10.1016/j.jat.2011.05.006

来源: Elsevier

【 摘 要 】

We construct a family of measures on R that are purely singular with respect to the Lebesgue measure, and yet exhibit universal sine kernel asymptotics in the bulk. The measures are best described via their Jacobi recursion coefficients: these are sparse perturbations of the recursion coefficients corresponding to Chebyshev polynomials of the second kind. We prove convergence of the renormalized Christoffel-Darboux kernel to the sine kernel for any sufficiently sparse decaying perturbation. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free