与希尔方程相关的随机奇异矩阵乘积的显方差CLT

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL Random Matrices-Theory and Applications Pub Date : 2020-12-03 DOI:10.1142/S2010326322500186

Phanuel Mariano, Hugo Panzo

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引用次数: 0

摘要

本文证明了一类随机奇异矩阵与Adams-Bloch-Lagarias研究的随机Hill方程乘积的中心极限定理(CLT)。CLT以矩阵项分布的显式方差公式为特征，这允许在某些示例中进行精确计算。我们的证明依赖于与[公式:见文本]相关序列理论的新联系，这也导致了一个有趣而精确的非简并条件。

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CLT with explicit variance for products of random singular matrices related to Hill’s equation

We prove a central limit theorem (CLT) for the product of a class of random singular matrices related to a random Hill’s equation studied by Adams–Bloch–Lagarias. The CLT features an explicit formula for the variance in terms of the distribution of the matrix entries and this allows for exact calculation in some examples. Our proof relies on a novel connection to the theory of [Formula: see text]-dependent sequences which also leads to an interesting and precise nondegeneracy condition.

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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.