Pair dependent linear statistics for CβE

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL Random Matrices-Theory and Applications Pub Date : 2020-12-17 DOI:10.1142/S2010326321500350

A. Aguirre, A. Soshnikov, Joshua Sumpter

引用次数: 6

Abstract

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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CβE的对相关线性统计量

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.90

自引率

11.10%

发文量

期刊介绍： Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.