Sine kernel asymptotics for a class of singular measures

Jonathan Breuer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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
Issue number10
StatePublished - Oct 2011

Bibliographical note

Funding Information:
We thank Yoram Last and Barry Simon for useful discussions. We also thank the referee for useful suggestions which improved the presentation of our results. This research was supported by The Israel Science Foundation (Grant no. 1105/10 ).


  • Christoffel-Darboux kernel
  • Singular continuous measure
  • Universality


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