The Nevai condition and a local law of large numbers for orthogonal polynomial ensembles

Jonathan Breuer, Maurice Duits*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We consider asymptotics of orthogonal polynomial ensembles, in the macroscopic and mesoscopic scales. We prove both global and local laws of large numbers under fairly weak conditions on the underlying measure μ. Our main tools are a general concentration inequality for determinantal point processes with a kernel that is a self-adjoint projection, and a strengthening of the Nevai condition from the theory of orthogonal polynomials.

Original languageAmerican English
Pages (from-to)441-484
Number of pages44
JournalAdvances in Mathematics
Volume265
DOIs
StatePublished - 10 Nov 2014

Keywords

  • Concentration inequalities
  • Determinantal point processes
  • Local law of large numbers
  • Nevai condition
  • Orthogonal polynomial ensembles
  • Orthogonal polynomials

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