Sine kernel asymptotics for a class of singular measures
Spectral Theory
2010-11-16 v1 Mathematical Physics
math.MP
Abstract
We construct a family of measures on that are purely singular with respect to 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.
Cite
@article{arxiv.1011.3159,
title = {Sine kernel asymptotics for a class of singular measures},
author = {Jonathan Breuer},
journal= {arXiv preprint arXiv:1011.3159},
year = {2010}
}