Related papers: Local semicircle law with imprimitive variance mat…

We study ensembles of random symmetric matrices whose entries exhibit certain correlations. Examples are distributions of Curie-Weiss-type. We provide a criterion on the correlations ensuring the validity of Wigner's semicircle law for the…

Consider a sample of a centered random vector with unit covariance matrix. We show that under certain regularity assumptions, and up to a natural scaling, the smallest and the largest eigenvalues of the empirical covariance matrix converge,…

We consider random Hermitian matrices with independent upper triangular entries. Wigner's semicircle law says that under certain additional assumptions, the empirical spectral distribution converges to the semicircle distribution. We…

We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the…

Let $U$ and $V$ be two independent $N$ by $N$ random matrices that are distributed according to Haar measure on $U(N)$. Let $\Sigma$ be a non-negative deterministic $N$ by $N$ matrix. The single ring theorem [26] asserts that the empirical…

This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for…

We analyse the spectrum of additive finite-rank deformations of $N \times N$ Wigner matrices $H$. The spectrum of the deformed matrix undergoes a transition, associated with the creation or annihilation of an outlier, when an eigenvalue…

This paper is concerned with extensions of the classical Mar\v{c}enko-Pastur law to time series. Specifically, $p$-dimensional linear processes are considered which are built from innovation vectors with independent, identically distributed…

The eigenvector empirical spectral distribution (VESD) is a useful tool in studying the limiting behavior of eigenvalues and eigenvectors of covariance matrices. In this paper, we study the convergence rate of the VESD of sample covariance…

We consider deformed sparse random matrices of the form $H= W+ \lambda V$, where $W$ is a real symmetric sparse random matrix, $V$ is a random or deterministic, real, diagonal matrix whose entries are independent of $W$, and $\lambda = O(1)…

In the present paper, we prove that under the assumption of the finite sixth moment for elements of a Wigner matrix, the convergence rate of its empirical spectral distribution to the Wigner semicircular law in probability is $O(n^{-1/2})$…

We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix…

We introduce kernel estimators for the semicircle law. In this first part of our general theory on the estimators, we prove the consistency and conduct simulation study to show the performance of the estimators. We also point out that…

We introduce a class of $M \times M$ sample covariance matrices $\mathcal Q$ which subsumes and generalizes several previous models. The associated population covariance matrix $\Sigma = \mathbb E \cal Q$ is assumed to differ from the…

We consider products of independent square non-Hermitian random matrices. More precisely, let X(1),...,X(n) be random matrices with independent entries (real or complex with independent real and imaginary parts) with zero mean and variance…

We review the application of the notion of local convergence on locally finite randomly rooted graphs, known as Benjamini-Schramm convergence, to the calculation of the global eigenvalue density of random matrices from the beta-Gaussian and…

Since E.P.Wigner (1958) established his famous semicircle law, lots of attention has been paid by physicists, probabilists and statisticians to study the asymptotic properties of the largest eigenvalues for random matrices. Bai and Yin…

In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…

We study the local semicircle law for Gaussian $\beta$-ensembles at the edge of the spectrum. We prove that at the almost optimal level of $n^{-2/3+\epsilon}$, the local semicircle law holds for all $\beta \geq 1$ at the edge. The proof of…

We prove the Marchenko-Pastur law for the eigenvalues of $p \times p$ sample covariance matrices in two new situations where the data does not have independent coordinates. In the first scenario - the block-independent model - the $p$…