分数布朗运动驱动的高维矩阵过程的特征值分布

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL Random Matrices-Theory and Applications Pub Date : 2024-05-20 DOI:10.1142/s2010326324500096

Jian Song, Jianfeng Yao, Wangjun Yuan

引用次数: 0

摘要

本文研究了一类 N×N 对称/赫米特随机矩阵的经验谱分布 {LN(t),t∈[0,T]}的高维行为，这些矩阵的条目由分数布朗运动驱动的随机微分方程的解生成，赫斯特参数为 H∈(1/2,1)。对于 Wigner 型矩阵，我们按照 [1] 中的方法得到了 C([0,T],P(ℝ) 中 {LN(t),t∈[0,T]}N∈ℕ 的几乎确定的相对紧凑性；］对于 Wishart 型矩阵，我们通过附录 B 中提供的严密性判据得到 {LN(t),t∈[0,T]}N∈ℕ 在 C([0,T],P(ℝ)) 上的严密性。{LN(t),t∈[0,T]}随 N→∞ 的极限也被表征。

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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Eigenvalue distributions of high-dimensional matrix processes driven by fractional Brownian motion

In this paper, we study high-dimensional behavior of empirical spectral distributions ${L_{N} (t), t \in [0, T]}$ for a class of $N \times N$ symmetric/Hermitian random matrices, whose entries are generated from the solution of stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H \in (1 / 2, 1)$ . For Wigner-type matrices, we obtain almost sure relative compactness of ${L_{N} (t), t \in [0, T]}_{N \in ℕ}$ in $C ([0, T], P (ℝ))$ following the approach in [1]; for Wishart-type matrices, we obtain tightness of ${L_{N} (t), t \in [0, T]}_{N \in ℕ}$ on $C ([0, T], P (ℝ))$ by tightness criterions provided in Appendix B. The limit of ${L_{N} (t), t \in [0, T]}$ as $N \to \infty$ is also characterized.

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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.