%0 Journal Article
%T A limiting random analytic function related to the CUE
%A Reda Chhaibi
%A Joseph Najnudel
%A Ashkan Nikeghbali
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1403.7814v1