Characteristic polynomials of random truncations: moments, duality and asymptotics

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2021-09-21 DOI:10.1142/s2010326322500496

A. Serebryakov, N. Simm, Guillaume Dubach

引用次数: 1

Abstract

We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite matrix size we calculate the moments in terms of hypergeometric functions of matrix argument and give explicit integral representations highlighting the duality between the moment and the matrix size as well as the duality between the orthogonal and symplectic cases. Asymptotic expansions in strong and weak non-unitarity regimes are obtained. Using the connection to matrix hypergeometric functions, we establish limit theorems for the log-modulus of the characteristic polynomial evaluated on the unit circle.

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随机截断的特征多项式:矩、对偶性和渐近性

研究了3个经典紧群O(N)、U(N)和Sp(2N)上截断Haar分布矩阵的特征多项式矩。对于有限大小的矩阵，我们用矩阵参数的超几何函数来计算矩，并给出了明确的积分表示，突出了矩与矩阵大小之间的对偶性以及正交和辛情况之间的对偶性。得到了强、弱非统一域的渐近展开式。利用与矩阵超几何函数的联系，建立了单位圆上特征多项式对数模的极限定理。

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.