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Central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7598-4521
2017 (English)In: Journal of The American Mathematical Society, ISSN 0894-0347, E-ISSN 1088-6834, Vol. 30, no 1, 27-66 p.Article in journal (Refereed) Published
Abstract [en]

We study fluctuations of linear statistics corresponding to smooth functions for certain biorthogonal ensembles. We study those biorthogonal ensembles for which the underlying biorthogonal family satisfies a finite term recurrence and describe the asymptotic fluctuations using right limits of the recurrence matrix. As a consequence, we show that whenever the right limit is a Laurent matrix, a central limit theorem holds. We will also discuss the implications for orthogonal polynomial ensembles. In particular, we obtain a central limit theorem for the orthogonal polynomial ensemble associated with any measure belonging to the Nevai class of an interval. Our results also extend previous results on unitary ensembles in the one-cut case. Finally, we will illustrate our results by deriving central limit theorems for the Hahn ensemble for lozenge tilings of a hexagon and for the Hermitian two matrix model.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2017. Vol. 30, no 1, 27-66 p.
Keyword [en]
Central limit theorems, linear statistics, random matrix theory, biorthogonal ensembles, Jacobi matrices, right limits, orthogonal polynomials
National Category
URN: urn:nbn:se:kth:diva-196583DOI: 10.1090/jams/854ISI: 000386135700002ScopusID: 2-s2.0-84992070748OAI: diva2:1047407
Knut and Alice Wallenberg Foundation, KAW 2010.0063Swedish Research Council, 2012-3128

QC 20161117

Available from: 2016-11-17 Created: 2016-11-17 Last updated: 2016-11-17Bibliographically approved

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Duits, Maurice
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