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arXiv · 1403.7814

A limiting random analytic function related to the CUE

Reda Chhaibi·Joseph Najnudel·Ashkan Nikeghbali
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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.

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Reda Chhaibi, Joseph Najnudel, Ashkan Nikeghbali. 2014-03-30. A limiting random analytic function related to the CUE. https://arxiv.org/abs/1403.7814

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