Universality of Mesoscopic Fluctuations for Orthogonal Polynomial Ensembles
2016 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 342, no 2, 491-531 p.Article in journal (Refereed) PublishedText
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 consequence we obtain a central limit theorem for the modified Jacobi Unitary Ensembles on all mesoscopic scales.
Place, publisher, year, edition, pages
Springer, 2016. Vol. 342, no 2, 491-531 p.
Mathematics Physical Sciences
IdentifiersURN: urn:nbn:se:kth:diva-184959DOI: 10.1007/s00220-015-2514-6ISI: 000371388500003ScopusID: 2-s2.0-84958176432OAI: oai:DiVA.org:kth-184959DiVA: diva2:917812
FunderSwedish Research Council, 2012-3128Knut and Alice Wallenberg Foundation, KAW 2010.0063
QC 201604072016-04-072016-04-072016-04-07Bibliographically approved