A limiting characteristic polynomial of some random matrix ensembles

A limiting characteristic polynomial of some random matrix ensembles

We prove a general limit theorem for the convergence of random entire functions with zeros that are point processes tending to the sine-kernel process. In particular we demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, a...

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Bibliographic Details
Published in:Annales Henri Poincaré
Main Authors: Chhaibi, Reda, Hovhannisyan, Emma, Najnudel, Joseph, Nikeghbali, Ashkan, Rodgers, Brad
Format: Journal Article
Language:English
Published: Springer Verlag 2019
Subjects:
Mathematical Physics
Mathematics
Probability
Representation Theory
Online Access:Get full text
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Description
Summary:We prove a general limit theorem for the convergence of random entire functions with zeros that are point processes tending to the sine-kernel process. In particular we demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-019-00769-4