Universality of Mesoscopic Fluctuations for Orthogonal Polynomial Ensembles

Jonathan Breuer*, Maurice Duits

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

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
Volume342
Issue number2
DOIs
StatePublished - 1 Mar 2016

Bibliographical note

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

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