与杨氏图相关的随机矩阵

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2023-01-31 DOI:10.1142/s2010326323500090

F. D. Cunden, M. Ligabò, Tommaso Monni

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引用次数: 1

摘要

研究了一类杨氏图形随机矩阵的奇异值。对于块状随机矩阵，奇异特征值的平方的经验分布几乎肯定地收敛到一个矩是加泰罗尼亚数的一般化的分布。极限分布是重新标度的独立Beta随机变量乘积的密度，其stieltje - cauchy变换具有超几何表示。在特殊情况下，我们分别恢复了方形和三角形随机矩阵的Marchenko-Pastur测度和Dykema-Haagerup测度。我们发现了两个复值随机变量的矩的进一步分解，它将Marcenko-Pastur定律的分解推广为独立的均匀随机变量和反正弦随机变量的乘积。

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Random matrices associated to Young diagrams

We consider the singular values of certain Young diagram shaped random matrices. For block-shaped random matrices, the empirical distribution of the squares of the singular eigenvalues converges almost surely to a distribution whose moments are a generalisation of the Catalan numbers. The limiting distribution is the density of a product of rescaled independent Beta random variables and its Stieltjes-Cauchy transform has a hypergeometric representation. In special cases we recover the Marchenko-Pastur and Dykema-Haagerup measures of square and triangular random matrices, respectively. We find a further factorisation of the moments in terms of two complex-valued random variables that generalises the factorisation of the Marcenko-Pastur law as product of independent uniform and arcsine random variables.

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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.