Sine kernel asymptotics for a class of singular measures

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Abstract

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.

Original languageAmerican English
Pages (from-to)1478-1491
Number of pages14
JournalJournal of Approximation Theory
Volume163
Issue number10
DOIs
StatePublished - Oct 2011

Keywords

  • Christoffel-Darboux kernel
  • Singular continuous measure
  • Universality

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics
  • Numerical Analysis
  • General Mathematics

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