Related papers: Limits of spiked random matrices I
In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues $\widehat{\lambda}_i$ and the generalized…
In this paper, the key objects of interest are the sequential covariance matrices $\mathbf{S}_{n,t}$ and their largest eigenvalues. Here, the matrix $\mathbf{S}_{n,t}$ is computed as the empirical covariance associated with observations…
We consider the eigenvalues of sample covariance matrices of the form $\mathcal{Q}=(\Sigma^{1/2}X)(\Sigma^{1/2}X)^*$. The sample $X$ is an $M\times N$ rectangular random matrix with real independent entries and the population covariance…
We study the limiting spectral distribution of sample covariance matrices $XX^T$, where $X$ are $p\times n$ random matrices with correlated entries, for the cases $p/n\to y\in [0,\infty)$. If $y>0$, we obtain the Mar\v{c}enko-Pastur…
We consider two models of one-dimensional discrete random Schrodinger operators (H_n \psi)_l ={\psi}_{l-1}+{\psi}_{l +1}+v_l {\psi}_l, {\psi}_0={\psi}_{n+1}=0 in the cases v_k=\sigma {\omega}_k/\sqrt{n} and v_k=\sigma {\omega}_k/ \sqrt{k}.…
We consider spectral properties of sparse sample covariance matrices, which includes biadjacency matrices of the bipartite Erd\H{o}s-R\'enyi graph model. We prove a local law for the eigenvalue density up to the upper spectral edge. Under a…
We investigate the asymptotic behavior of the eigenvalues of spiked perturbations of Wigner matrices when the dimension goes to infinity. The entries of the Hermitian Wigner matrix have a distribution which is symmetric and satisfies a…
We use tools from random matrix theory to study the multi-spiked tensor model, i.e., a rank-$r$ deformation of a symmetric random Gaussian tensor. In particular, thanks to the nature of local optimization methods used to find the maximum…
We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the spike magnitude of leading eigenvalues, sample size, and dimensionality. This…
This is the second part of a study of the limiting distributions of the top eigenvalues of a Hermitian matrix model with spiked external source under a general external potential. The case when the external source is of rank one was…
The correlated Wishart model provides a standard tool for the analysis of correlations in a rich variety of systems. Although much is known for complex correlation matrices, the empirically much more important real case still poses…
We consider sample covariance matrices of the form $\mathcal{Q}=(\Sigma^{1/2}X)(\Sigma^{1/2} X)^*$, where the sample $X$ is an $M\times N$ random matrix whose entries are real independent random variables with variance $1/N$ and where…
The extreme-value statistics of the entanglement spectrum in disordered spin chains possessing a many-body localization transition is examined. It is expected that eigenstates in the metallic or ergodic phase, behave as random states and…
The Tracy-Widom distributions are among the most famous laws in probability theory, partly due to their connection with Wigner matrices. In particular, for $A=\frac{1}{\sqrt{n}}(a_{ij})_{1 \leq i,j \leq n} \in \mathbb{R}^{n \times n}$…
This paper investigates limiting properties of eigenvalues of multivariate sample spatial-sign covariance matrices when both the number of variables and the sample size grow to infinity. The underlying p-variate populations are general…
The large-matrix limit laws of the rescaled largest eigenvalue of the orthogonal, unitary, and symplectic $n$-dimensional Gaussian ensembles -- and of the corresponding Laguerre ensembles (Wishart distributions) for various regimes of the…
We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. In this setting, the support of the limiting eigenvalue distribution may have several connected components.…
In this article we show the existence of limiting spectral distribution of a symmetric random matrix whose entries come from a stationary Gaussian process with covariances satisfying a summability condition. We provide an explicit…
In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently…
We consider a more generalized spiked covariance matrix $\Sigma$, which is a general non-definite matrix with the spiked eigenvalues scattered into a few bulks and the largest ones allowed to tend to infinity. By relaxing the matching of…