Sine kernel asymptotics for a class of singular measures

Details Sine kernel asymptotics for a class of singular measures Sine kernel asymptotics for a class of singular measures

2010-11-13

arxiv.org/abs/1011.3159v1

Mathematics

Spectral Theory

Scientific paper

We construct a family of measures on $\bbR$ 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.

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