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The Nevai condition and a local law of large numbers for orthogonal polynomial ensembles
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-7598-4521
2014 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 265, 441-484 p.Article in journal (Refereed) Published
Abstract [en]

We consider asymptotics of orthogonal polynomial ensembles, in the macroscopic and mesoscopic scales. We prove both global and local laws of large numbers under fairly weak conditions on the underlying measure mu. Our main tools are a general concentration inequality for determinantal point processes with a kernel that is a self-adjoint projection, and a strengthening of the Nevai condition from the theory of orthogonal polynomials.

Place, publisher, year, edition, pages
2014. Vol. 265, 441-484 p.
Keyword [en]
Determinantal point processes, Orthogonal polynomial ensembles, Concentration inequalities, Local law of large numbers, Orthogonal polynomials, Nevai condition
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-154365DOI: 10.1016/j.aim.2014.07.026ISI: 000342035000014Scopus ID: 2-s2.0-84906739478OAI: oai:DiVA.org:kth-154365DiVA: diva2:757114
Funder
Knut and Alice Wallenberg Foundation, KAW 2010.0063Swedish Research Council, 2012-3128
Note

QC 20141021

Available from: 2014-10-21 Created: 2014-10-20 Last updated: 2017-12-05Bibliographically approved

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Duits, Maurice

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