Random Matrices-Theory and Applications最新文献

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Tail Bounds on the Spectral Norm of Sub-Exponential Random Matrices 次指数随机矩阵谱范数的尾界

4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications

Pub Date : 2023-11-01 DOI: 10.1142/s2010326323500132

Guozheng Dai, Zhonggen Su, Hanchao Wang

Let $X$ be an $ntimes n$ symmetric random matrix with independent but non-identically distributed entries. The deviation inequalities of the spectral norm of $X$ with Gaussian entries have been obtained by using the standard concentration of Gaussian measure results. This paper establishes an upper tail bound of the spectral norm of $X$ with sub-Exponential entries. Our method relies upon a crucial ingredient of a novel chaining argument that essentially involves both the particular structure of the sets used for the chaining and the distribution of coordinates of a point on the unit sphere.

引用次数: 2

Finite Rank Perturbations of Heavy-Tailed Wigner Matrices 重尾Wigner矩阵的有限秩摄动

4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications

Pub Date : 2023-10-27 DOI: 10.1142/s2010326323500119

Simona Diaconu

One-rank perturbations of Wigner matrices have been closely studied: let [Formula: see text] with [Formula: see text] symmetric, [Formula: see text] i.i.d. with centered standard normal distributions, and [Formula: see text] It is well known [Formula: see text] the largest eigenvalue of [Formula: see text] has a phase transition at [Formula: see text]: when [Formula: see text] [Formula: see text] whereas for [Formula: see text] [Formula: see text] Under more general conditions, the limiting behavior of [Formula: see text] appropriately normalized, has also been established: it is normal if [Formula: see text] or the convolution of the law of [Formula: see text] and a Gaussian distribution if [Formula: see text] is concentrated on one entry. These convergences require a finite fourth moment, and this paper considers situations violating this condition. For symmetric distributions [Formula: see text] heavy-tailed with index [Formula: see text] the fluctuations are shown to be universal and dependent on [Formula: see text] but not on [Formula: see text] whereas a subfamily of the edge case [Formula: see text] displays features of both the light- and heavy-tailed regimes: two limiting laws emerge and depend on whether [Formula: see text] is localized, each presenting a continuous phase transition at [Formula: see text] respectively. These results build on our previous work which analyzes the asymptotic behavior of [Formula: see text] in the aforementioned subfamily.

魏格纳矩阵的阶扰动密切研究:让[公式:看到文本][公式:看到文本]对称,[公式:看到文本]i.i.d.集中标准正态分布,和[公式:看到文本]众所周知[公式:看到文本]最大的特征值公式:看到文本有相变(公式:看到文本):当[公式:看到文本][公式:看到文本]而对于[公式:看到文本][公式:在更一般的条件下，[公式:见文]的极限行为也得到了适当的归一化:如果[公式:见文]是正态的，如果[公式:见文]集中在一个条目上，则[公式:见文]与[公式:见文]定律的卷积是高斯分布。这些收敛需要有限的第四矩，本文考虑了违反这个条件的情况。对于对称分布[公式:见文]，有索引的重尾[公式:见文]，涨落是普遍的，依赖于[公式:见文]，但不依赖于[公式:见文]，而边缘情况的一个亚族[公式:见文]显示了轻尾和重尾状态的特征:出现了两个极限定律，并取决于[公式:见文]是否局部化，每个定律分别在[公式:见文]处呈现连续相变。这些结果建立在我们之前的工作基础上，该工作分析了上述子族中的[公式:见文本]的渐近行为。

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引用次数: 4

Strong limit theorem for largest entry of large-dimensional random tensor 大维随机张量最大入口的强极限定理

4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications

Pub Date : 2023-10-12 DOI: 10.1142/s2010326323500120

Xue Ding

Suppose that [Formula: see text] are i.i.d. copies of random vector [Formula: see text]. Let [Formula: see text] then the random tensor product constructed by [Formula: see text] is defined by [Formula: see text] In this paper, we obtain the strong limit theorems of the largest entry of large-dimensional random tensor product [Formula: see text] under two high-dimensional settings the polynomial rate and the exponential rate. The conclusions are established under weaker moment condition than the exist papers and the relationship between [Formula: see text] and [Formula: see text] is more flexible.

假设[公式:见文本]是随机向量[公式:见文本]的i.d个副本。设[公式:见文]，则由[公式:见文]构造的随机张量积由[公式:见文]定义。本文在多项式率和指数率两种高维设置下，得到了大维随机张量积[公式:见文]的最大入口的强极限定理。结论是在较弱的力矩条件下建立的，且[公式:见文]与[公式:见文]之间的关系更加灵活。

引用次数: 0

Rank 1 perturbations in random matrix theory — A review of exact results 随机矩阵理论中的秩1扰动——精确结果综述

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications

Pub Date : 2023-08-19 DOI: 10.1142/s2010326323300012

Peter J. Forrester

A number of random matrix ensembles permitting exact determination of their eigenvalue and eigenvector statistics maintain this property under a rank $1$ perturbation. Considered in this review are the additive rank $1$ perturbation of the Hermitian Gaussian ensembles, the multiplicative rank $1$ perturbation of the Wishart ensembles, and rank $1$ perturbations of Hermitian and unitary matrices giving rise to a two-dimensional support for the eigenvalues. The focus throughout is on exact formulas, which are typically the result of various integrable structures. The simplest is that of a determinantal point process, with others relating to partial differential equations implied by a formulation in terms of certain random tridiagonal matrices. Attention is also given to eigenvector overlaps in the setting of a rank $1$ perturbation.

允许精确确定其特征值和特征向量统计的许多随机矩阵系综在秩1扰动下保持这种性质。在这篇综述中，考虑了埃尔米特-高斯系综的加性秩1扰动、Wishart系综的乘性秩1微扰以及埃尔米特矩阵和酉矩阵的秩1扰动，这些扰动产生了对特征值的二维支持。贯穿始终的焦点是精确公式，它通常是各种可积结构的结果。最简单的是行列式点过程，其他的则与偏微分方程有关，这些偏微分方程是由某些随机三对角矩阵的公式所暗示的。还注意在秩1扰动的设置中的特征向量重叠。

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引用次数: 6

Limiting spectral distribution of stochastic block model 随机块段模型的极限谱分布

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications

Pub Date : 2023-07-18 DOI: 10.1142/s2010326323500089

Giap Van Su, May-Ru Chen, Mei-Hui Guo, Hao-Wei Huang

The stochastic block model (SBM) is an extension of the Erdős–Rényi graph and has applications in numerous fields, such as data analysis, recovering community structure in graph data and social networks. In this paper, we consider the normal central SBM adjacency matrix with $K$ communities of arbitrary sizes. We derive an explicit formula for the limiting empirical spectral density function when the size of the matrix tends to infinity. We also obtain an upper bound for the operator norm of such random matrices by means of the Stieltjes transform and random matrix theory.

随机块模型（SBM）是Erdõs–Rényi图的扩展，在数据分析、恢复图数据中的社区结构和社交网络等众多领域都有应用。在本文中，我们考虑具有任意大小的K个社区的正规中心SBM邻接矩阵。当矩阵的大小趋于无穷大时，我们导出了极限经验谱密度函数的一个显式公式。利用Stieltjes变换和随机矩阵理论，得到了这类随机矩阵的算子范数的上界。

引用次数: 0

Corrigendum: Sampling distributions of optimal portfolio weights and characteristics in small and large dimensions 更正:最优投资组合权重和特征的小、大维度抽样分布

4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications

Pub Date : 2023-07-01 DOI: 10.1142/s2010326323920016

Taras Bodnar, Holger Dette, Nestor Parolya, Erik Thorsén

Random Matrices: Theory and ApplicationsOnline Ready Free AccessCorrigendum: Sampling distributions of optimal portfolio weights and characteristics in small and large dimensionsis erratum ofSampling distributions of optimal portfolio weights and characteristics in small and large dimensionsTaras Bodnar, Holger Dette, Nestor Parolya, and Erik ThorsénTaras BodnarDepartment of Mathematics, Stockholm University, Stockholm, Sweden, Holger DetteDepartment of Mathematics, Ruhr University Bochum, D-44870 Bochum, Germany, Nestor ParolyaDelft Institute of Applied Mathematics, Delft University of Technology, Delft, The NetherlandsCorresponding author., and Erik ThorsénDepartment of Mathematics, Stockholm University, Stockholm, Swedenhttps://doi.org/10.1142/S2010326323920016Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail FiguresReferencesRelatedDetailsRelated articlesSampling distributions of optimal portfolio weights and characteristics in small and large dimensions7 Jun 2021Random Matrices: Theory and Applications Recommended Online Ready Metrics History Received 16 April 2023 Accepted 31 May 2023 Published: 11 July 2023 PDF download

随机矩阵:理论与应用最优投资组合权值和特征在小维和大维的抽样分布的勘错staras Bodnar、Holger Dette、Nestor Parolya和Erik thorssamn taras bodnar瑞典斯德哥尔摩大学数学系Holger dethe德国波洪鲁尔大学数学系D-44870波洪Nestor ParolyaDelft应用数学研究所代尔夫特理工大学，荷兰代尔夫特。瑞典斯德哥尔摩大学数学系，瑞典斯德哥尔摩https://doi.org/10.1142/S2010326323920016Cited by:0前一PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack citationsrecommended to Library ShareShare onFacebookTwitterLinked InRedditEmail figurereferencesrelateddetailsrelated articles最优投资组合权重和特征的采样分布在小维度和大维度7 Jun 2021随机矩阵:理论与应用推荐在线就绪度量历史接收2023年4月16日接收2023年5月31日发布:2023年7月11日PDF下载

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引用次数: 0

Matrix deviation inequality for ℓp-norm 的矩阵偏差不等式ℓp-范数

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications

Pub Date : 2023-06-15 DOI: 10.1142/s2010326323500077

Yuan-Chung Sheu, Te-Chun Wang

Motivated by the general matrix deviation inequality for i.i.d. ensemble Gaussian matrix [R. Vershynin, High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge University Press, 2018), doi:10.1017/9781108231596 of Theorem 11.1.5], we show that this property holds for the $ℓ_{p}$ -norm with $1 \leq p < \infty$ and i.i.d. ensemble sub-Gaussian matrices, i.e. random matrices with i.i.d. mean-zero, unit variance, sub-Gaussian entries. As a consequence of our result, we establish the Johnson–Lindenstrauss lemma from $ℓ_{2}^{n}$ -space to $ℓ_{p}^{m}$ -space for all i.i.d. ensemble sub-Gaussian matrices.

受i.i.d.系综高斯矩阵的一般矩阵偏差不等式[R.Vershynin，《高维概率：数据科学应用导论》，剑桥统计与概率数学系列（剑桥大学出版社，2018），doi:10.1017/9781108231596 of Theorem 11.1.5]的启发，我们证明了这一性质适用于ℓ1≤p<；∞的p-范数和i.i.d.系综亚高斯矩阵，即具有i.i.d.均值为零、单位方差、亚高斯项的随机矩阵。由于我们的结果，我们从中建立了Johnson–Lindenstrauss引理ℓ2n空间到ℓpm空间。

引用次数: 0

Random matrices associated to Young diagrams 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

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.

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。

引用次数: 1

The moderate deviation principles of likelihood ratio tests under alternative hypothesis 备择假设下似然比检验的适度偏差原则

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications

Pub Date : 2022-12-15 DOI: 10.1142/s201032632350003x

Yansong Bai, Yong Zhang

引用次数: 0

Asymptotic Properties of GEE with Diverging Dimension of Covariates 协变量维数发散的GEE的渐近性质

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications

Pub Date : 2022-10-10 DOI: 10.1142/s2010326323500016

Qibing Gao, Chunhua Zhu, Yi Yao

引用次数: 0

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