A limiting random analytic function related to the CUE
Probability
2014-04-01 v1
Abstract
We show in this paper that, when properly rescaled in time and in space, the characteristic polynomial of a random unitary matrix converges almost surely to a random analytic function whose zeros, which are on the real line, form a determinantal point process with sine kernel. We prove this result in the framework of virtual isometries to circumvent the fact that the rescaled characteristic polynomial does not even have a moment of order one, hence making the classical techniques of random matrix theory difficult to apply.
Cite
@article{arxiv.1403.7814,
title = {A limiting random analytic function related to the CUE},
author = {Reda Chhaibi and Joseph Najnudel and Ashkan Nikeghbali},
journal= {arXiv preprint arXiv:1403.7814},
year = {2014}
}