Scaling Limits of Jacobi Matrices and the Christoffel–Darboux Kernel

Jonathan Breuer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study scaling limits of deterministic Jacobi matrices, centered around a fixed point x, and their connection to the scaling limits of the Christoffel–Darboux kernel at that point. We show that in the case when the orthogonal polynomials are bounded at x, a subsequential limit always exists and can be expressed as a canonical system. We further show that under weak conditions on the associated measure, bulk universality of the CD kernel is equivalent to the existence of a limit of a particular explicit form.

Original languageAmerican English
Pages (from-to)349-379
Number of pages31
JournalConstructive Approximation
Issue number2
StatePublished - Apr 2021

Bibliographical note

Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.


  • Canonical systems
  • Christoffel–Darboux kernel
  • Scaling limit
  • Universality


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