A limiting characteristic polynomial of some random matrix ensembles

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

Published 2017-07-31Version 1

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.