CβE的对相关线性统计量

Pub Date : 2020-12-17 DOI:10.1142/S2010326321500350

A. Aguirre, A. Soshnikov, Joshua Sumpter

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引用次数: 6

摘要

对于充分光滑的测试函数[公式:见文]和[公式:见文]的随机矩阵的圆形[公式:见文]-集合(C[公式:见文]E)，我们研究了形式为[公式:见文]的对计数统计量的极限分布。对于[公式:见文]和[公式:见文]，我们的结果受到Montgomery关于黎曼zeta函数零对相关的经典结果的启发。

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Pair dependent linear statistics for CβE

We study the limiting distribution of a pair counting statistics of the form [Formula: see text] for the circular [Formula: see text]-ensemble (C[Formula: see text]E) of random matrices for sufficiently smooth test function [Formula: see text] and [Formula: see text] For [Formula: see text] and [Formula: see text] our results are inspired by a classical result of Montgomery on pair correlation of zeros of Riemann zeta function.

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