Universality of Mesoscopic Fluctuations for Orthogonal Polynomial Ensembles

Jonathan Breuer*, Maurice Duits

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We prove that the fluctuations of mesoscopic linear statistics for orthogonal polynomial ensembles are universal in the sense that two measures with asymptotic recurrence coefficients have the same asymptotic mesoscopic fluctuations (under an additional assumption on the local regularity of one of the measures). The convergence rate of the recurrence coefficients determines the range of scales on which the limiting fluctuations are identical. Our main tool is an analysis of the Green’s function for the associated Jacobi matrices.As a particular consequencewe obtain a central limit theorem for the modified Jacobi Unitary Ensembles on all mesoscopic scales.

Original languageAmerican English
Pages (from-to)491-531
Number of pages41
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - 1 Mar 2016

Bibliographical note

Funding Information:
Maurice Duits: Supported in part by the Grant KAW 2010.0063 from the Knut and Alice Wallenberg Foundation and by the Swedish Research Council (VR) Grant No. 2012-3128.

Funding Information:
Jonathan Breuer: Supported in part by the US-Israel Binational Science Foundation (BSF) Grant No. 2010348 and by the Israel Science Foundation (ISF) Grant No. 1105/10.

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.


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