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 language | English |
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Pages (from-to) | 1093-1119 |
Number of pages | 26 |
Journal | Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques |
Volume | 20 |
Issue number | 4 |
Early online date | 31 Jan 2019 |
DOIs | |
Publication status | Published - 31 Jan 2019 |