Random Matrices-Theory and Applications最新文献_第7页

Spectral properties for the Laplacian of a generalized Wigner matrix 广义Wigner矩阵拉普拉斯算子的谱性质

IF 0.9 4区数学

Random Matrices-Theory and Applications Pub Date : 2020-11-16 DOI: 10.1142/s2010326322500265

Anirban Chatterjee, R. S. Hazra

引用次数: 5

High-dimensional regimes of non-stationary Gaussian correlated Wishart matrices 非平稳高斯相关Wishart矩阵的高维状态

IF 0.9 4区数学

Random Matrices-Theory and Applications Pub Date : 2020-11-02 DOI: 10.1142/S201032632250006X

S. Bourguin, Thanh Dang

{"title":"High-dimensional regimes of non-stationary Gaussian correlated Wishart matrices","authors":"S. Bourguin, Thanh Dang","doi":"10.1142/S201032632250006X","DOIUrl":"https://doi.org/10.1142/S201032632250006X","url":null,"abstract":"We study the high-dimensional asymptotic regimes of correlated Wishart matrices [Formula: see text], where [Formula: see text] is a [Formula: see text] Gaussian random matrix with correlated and non-stationary entries. We prove that under different normalizations, two distinct regimes emerge as both [Formula: see text] and [Formula: see text] grow to infinity. The first regime is the one of central convergence, where the law of the properly renormalized Wishart matrices becomes close in Wasserstein distance to that of a Gaussian orthogonal ensemble matrix. In the second regime, a non-central convergence happens, and the law of the normalized Wishart matrices becomes close in Wasserstein distance to that of the so-called Rosenblatt–Wishart matrix recently introduced by Nourdin and Zheng. We then proceed to show that the convergences stated above also hold in a functional setting, namely as weak convergence in [Formula: see text]. As an application of our main result (in the central convergence regime), we show that it can be used to prove convergence in expectation of the empirical spectral distributions of the Wishart matrices to the semicircular law. Our findings complement and extend a rich collection of results on the study of the fluctuations of Gaussian Wishart matrices, and we provide explicit examples based on Gaussian entries given by normalized increments of a bi-fractional or a sub-fractional Brownian motion.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90840434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

COVARIANCE KERNEL OF LINEAR SPECTRAL STATISTICS FOR HALF-HEAVY TAILED WIGNER MATRICES 半重尾wigner矩阵线性谱统计量的协方差核

IF 0.9 4区数学

Random Matrices-Theory and Applications Pub Date : 2020-10-08 DOI: 10.1142/s201032632250054x

A. Lodhia, A. Maltsev

引用次数: 1

Joint global fluctuations of complex Wigner and deterministic matrices 复Wigner矩阵与确定性矩阵的联合全局波动

IF 0.9 4区数学

Random Matrices-Theory and Applications Pub Date : 2020-10-06 DOI: 10.1142/S2010326322500150

C. Male, J. Mingo, S. P'ech'e, R. Speicher

引用次数: 7

Robust feature screening for multi-response trans-elliptical regression model with ultrahigh-dimensional covariates 超高维协变量多响应跨椭圆回归模型的鲁棒特征筛选

IF 0.9 4区数学

Random Matrices-Theory and Applications Pub Date : 2020-10-01 DOI: 10.1142/s2010326321500015

Yong He, Hao Sun, Jiadong Ji, Xinsheng Zhang

{"title":"Robust feature screening for multi-response trans-elliptical regression model with ultrahigh-dimensional covariates","authors":"Yong He, Hao Sun, Jiadong Ji, Xinsheng Zhang","doi":"10.1142/s2010326321500015","DOIUrl":"https://doi.org/10.1142/s2010326321500015","url":null,"abstract":"In this paper, we innovatively propose an extremely flexible semi-parametric regression model called Multi-response Trans-Elliptical Regression (MTER) Model, which can capture the heavy-tail characteristic and tail dependence of both responses and covariates. We investigate the feature screening procedure for the MTER model, in which Kendall’ tau-based canonical correlation estimators are proposed to characterize the correlation between each transformed predictor and the multivariate transformed responses. The main idea is to substitute the classical canonical correlation ranking index in [X. B. Kong, Z. Liu, Y. Yao and W. Zhou, Sure screening by ranking the canonical correlations, TEST 26 (2017) 1–25] by a carefully constructed non-parametric version. The sure screening property and ranking consistency property are established for the proposed procedure. Simulation results show that the proposed method is much more powerful to distinguish the informative features from the unimportant ones than some state-of-the-art competitors, especially for heavy-tailed distributions and high-dimensional response. At last, a real data example is given to illustrate the effectiveness of the proposed procedure.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84038643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Empirical likelihood for high-dimensional partially functional linear model 高维部分泛函线性模型的经验似然

IF 0.9 4区数学

Random Matrices-Theory and Applications Pub Date : 2020-10-01 DOI: 10.1142/S2010326320500173

Zhiqiang Jiang, Zhensheng Huang, Guoliang Fan

引用次数: 1

No eigenvalues outside the support of the limiting spectral distribution of quaternion sample covariance matrices 在四元数样本协方差矩阵的极限谱分布支持之外没有特征值

IF 0.9 4区数学

Random Matrices-Theory and Applications Pub Date : 2020-10-01 DOI: 10.1142/s2010326321500039

Huiqin Li

引用次数: 6

Large deviations for spectral measures of some spiked matrices 某些加标矩阵的光谱测量偏差较大

IF 0.9 4区数学

Random Matrices-Theory and Applications Pub Date : 2020-09-26 DOI: 10.1142/s2010326322500393

Nathan Noiry, A. Rouault

引用次数: 1

Differential and difference equations for recurrence coefficients of orthogonal polynomials with hypergeometric weights and Bäcklund transformations of the sixth Painlevé equation 超几何权重正交多项式递推系数的微分与差分方程及第六届painlevleve方程的Bäcklund变换

IF 0.9 4区数学

Random Matrices-Theory and Applications Pub Date : 2020-09-24 DOI: 10.1142/s2010326321500295

Jie Hu, G. Filipuk, Yang Chen

{"title":"Differential and difference equations for recurrence coefficients of orthogonal polynomials with hypergeometric weights and Bäcklund transformations of the sixth Painlevé equation","authors":"Jie Hu, G. Filipuk, Yang Chen","doi":"10.1142/s2010326321500295","DOIUrl":"https://doi.org/10.1142/s2010326321500295","url":null,"abstract":"It is known from [G. Filipuk and W. Van Assche, Discrete orthogonal polynomials with hypergeometric weights and Painlevé VI, Symmetry Integr. Geom. Methods Appl. 14 (2018), Article ID: 088, 19 pp.] that the recurrence coefficients of discrete orthogonal polynomials on the nonnegative integers with hypergeometric weights satisfy a system of nonlinear difference equations. There is also a connection to the solutions of the [Formula: see text]-form of the sixth Painlevé equation (one of the parameters of the weights being the independent variable in the differential equation) [G. Filipuk and W. Van Assche, Discrete orthogonal polynomials with hypergeometric weights and Painlevé VI, Symmetry Integr. Geom. Methods Appl. 14 (2018), Article ID: 088, 19 pp.]. In this paper, we derive a second-order nonlinear difference equation from the system and present explicit formulas showing how this difference equation arises from the Bäcklund transformations of the sixth Painlevé equation. We also present an alternative way to derive the connection between the recurrence coefficients and the solutions of the sixth Painlevé equation.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86947402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Global eigenvalue fluctuations of random biregular bipartite graphs 随机双正则二部图的全局特征值波动

IF 0.9 4区数学

Random Matrices-Theory and Applications Pub Date : 2020-08-26 DOI: 10.1142/s2010326323500041

Ioana Dumitriu, Yizhe Zhu

引用次数: 5