Universality Limits in the Bulk for Arbitrary Measures on Compact Sets

@inproceedings{Lubinsky2007UniversalityLI,
  title={Universality Limits in the Bulk for Arbitrary Measures on Compact Sets},
  author={Doron S. Lubinsky},
  year={2007}
}
We present a new method for establishing universality limits in the bulk, based on the theory of entire functions of exponential type. Let be a measure on a compact subset of the real line. Assume that is absolutely continuous in a neighborhood of some point x in the support, and that 0 is bounded above and below near x, which is assumed to be a Lebesgue point of 0. Then universality holds at x i¤ it holds "along the diagonal", that is lim n!1 Kn x+ a n ; x+ a n Kn (x; x) = 1; for all real a… CONTINUE READING
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