A limiting characteristic polynomial of some random matrix ensembles

Reda Chhaibi, Emma Hovhannisyan, Joseph Najnudel, Ashkan Nikeghbali, Brad Rodgers

Research output: Contribution to journalArticle (Academic Journal)peer-review

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.
Original languageEnglish
Pages (from-to)1093-1119
Number of pages26
JournalAnnales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Volume20
Issue number4
Early online date31 Jan 2019
DOIs
Publication statusPublished - 31 Jan 2019

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