一个与CUE有关的极限随机解析函数
A limiting random analytic function related to the CUE
摘要：
本文证明了，当在时间和空间上适当地重新标度时，随机酉矩阵的特征多项式几乎必然收敛于一个随机解析函数，该函数的零点在实直线上形成一个具有正弦核的行列式点过程.我们证明了这一结果的框架中的虚拟等距规避的事实，即重新缩放的特征多项式甚至没有一个时刻的顺序，从而使随机矩阵理论的经典技术难以应用。
英文摘要：
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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