Related papers: A unified matrix model including both CCA and F ma…

We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any polynomial potential. beta is a positive number, so not…

Consider two random vectors $\mathbf C_1^{1/2}\mathbf x \in \mathbb R^p$ and $\mathbf C_2^{1/2}\mathbf y\in \mathbb R^q$, where the entries of $\mathbf x$ and $\mathbf y$ are i.i.d. random variables with mean zero and variance one, and…

We consider the extreme eigenvalues of the sample covariance matrix $Q=YY^*$ under the generalized elliptical model that $Y=\Sigma^{1/2}XD.$ Here $\Sigma$ is a bounded $p \times p$ positive definite deterministic matrix representing the…

In this paper, we study the largest eigenvalues of sample covariance matrices with elliptically distributed data. We consider the sample covariance matrix $Q=YY^*,$ where the data matrix $Y \in \mathbb{R}^{p \times n}$ contains i.i.d.…

For $N,n\in\mathbb N$, consider the sample covariance matrix $$S_N(T)=\frac{1}{N}XX^*$$ from a data set $X=C_N^{1/2}ZT_n^{1/2}$, where $Z=(Z_{i,j})$ is a $N\times n$ matrix having i.i.d. entries with mean zero and variance one, and $C_N,…

Let $\boldsymbol{\Sigma}_N$ be a $M \times N$ random matrix defined by $\boldsymbol{\Sigma}_N = \mathbf{B}_N + \sigma \mathbf{W}_N$ where $\mathbf{B}_N$ is a uniformly bounded deterministic matrix and where $\mathbf{W}_N$ is an independent…

Let $G=G(n,p_n)$ be a homogeneous Erd\"os-R\'enyi graph, and $A$ its adjacency matrix with eigenvalues $\lambda_1(A) \geq \lambda_2(A) \geq ... \geq \lambda_n(A).$ Local laws have been used to show that $lambda_2(A)$ can exhibit…

We consider the limiting location and limiting distribution of the largest eigenvalue in real symmetric ($\beta$ = 1), Hermitian ($\beta$ = 2), and Hermitian self-dual ($\beta$ = 4) random matrix models with rank 1 external source. They are…

Let $\mathbf{X}_n=(x_{ij})$ be a $k \times n$ data matrix with complex-valued, independent and standardized entries satisfying a Lindeberg-type moment condition. We consider simultaneously $R$ sample covariance matrices…

Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

We consider fluctuations of the largest eigenvalues of the random matrix model $A+UBU^{*}$ where $A$ and $B$ are $N \times N$ deterministic Hermitian (or symmetric) matrices and $U$ is a Haar-distributed unitary (or orthogonal) matrix. We…

We consider continuous-time models with a large panel of moment conditions, where the structural parameter depends on a set of characteristics, whose effects are of interest. The leading example is the linear factor model in financial…

Let $X$ be a symmetric, isotropic random vector in $\mathbb{R}^m$ and let $X_1...,X_n$ be independent copies of $X$. We show that under mild assumptions on $\|X\|_2$ (a suitable thin-shell bound) and on the tail-decay of the marginals…

We study the largest eigenvalue of a Gaussian random symmetric matrix $X_n$, with zero-mean, unit variance entries satisfying the condition $\sup_{(i, j) \ne (i', j')}|\mathbb{E}[X_{ij} X_{i'j'}]| = O(n^{-(1 + \varepsilon)})$, where…

Let X be a n*p matrix and l_1 the largest eigenvalue of the covariance matrix X^{*}*X. The "null case" where X_{i,j} are independent Normal(0,1) is of particular interest for principal component analysis. For this model, when n, p tend to…

We compute the limiting distributions of the largest eigenvalue of a complex Gaussian sample covariance matrix when both the number of samples and the number of variables in each sample become large. When all but finitely many, say $r$,…

We propose a two-sample test for covariance matrices in the high-dimensional regime, where the dimension diverges proportionally to the sample size. Our hybrid test combines a Frobenius-norm-based statistic as considered in Li and Chen…

We study the statistics of the largest eigenvalue lambda_max of N x N random matrices with unit variance, but power-law distributed entries, P(M_{ij})~ |M_{ij}|^{-1-mu}. When mu > 4, lambda_max converges to 2 with Tracy-Widom fluctuations…

We consider a multivariate linear response regression in which the number of responses and predictors is large and comparable with the number of observations, and the rank of the matrix of regression coefficients is assumed to be small. We…

We apply the method of determinants to study the distribution of the largest singular values of large $ m \times n $ real rectangular random matrices with independent Cauchy entries. We show that statistical properties of the (rescaled by a…