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The limiting characteristic polynomial of classical random matrix ensembles


Chhaibi, Reda; Hovhannisyan, Emma; Najnudel, Joseph; Nikeghbali, Ashkan; Rodgers, Brad (2019). The limiting characteristic polynomial of classical random matrix ensembles. Annales Henri Poincare, 20(4):1093-1119.

Abstract

We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the Gaussian Unitary Ensemble. In fact, the result is the by-product of a general limit theorem for the convergence of random entire functions whose zeros present a simple regularity property.

Abstract

We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the Gaussian Unitary Ensemble. In fact, the result is the by-product of a general limit theorem for the convergence of random entire functions whose zeros present a simple regularity property.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:910 Geography & travel
Scopus Subject Areas:Physical Sciences > Statistical and Nonlinear Physics
Physical Sciences > Nuclear and High Energy Physics
Physical Sciences > Mathematical Physics
Uncontrolled Keywords:Nuclear and High Energy Physics, Mathematical Physics, Statistical and Nonlinear Physics
Language:English
Date:1 April 2019
Deposited On:11 Apr 2019 13:20
Last Modified:30 May 2020 11:28
Publisher:Birkhaeuser Science
ISSN:1424-0661
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00023-019-00769-4

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