Related papers: Beta Laguerre ensembles in global regime

In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given by Dumitriu and Edelman. We prove here the convergence of the distribution of the eigenvalues and compute the limiting distributions…

An invariant ensemble of $N\times N$ random matrices can be characterised by a joint distribution for eigenvalues $P(\lambda_1,\cdots,\lambda_N)$. The study of the distribution of linear statistics, i.e. of quantities of the form…

Consider a high-dimensional Wishart matrix $\bd{W}=\bd{X}^T\bd{X}$ where the entries of $\bd{X}$ are i.i.d. random variables with mean zero, variance one, and a finite fourth moment $\eta$. Motivated by problems in signal processing and…

For the orthogonal-unitary and symplectic-unitary transitions in random matrix theory, the general parameter dependent distribution between two sets of eigenvalues with two different parameter values can be expressed as a quaternion…

We consider $n\times n$ random matrices $M_{n}=\sum_{\alpha =1}^{m}{\tau _{\alpha }}\mathbf{y}_{\alpha }\otimes \mathbf{y}_{\alpha }$, where $\tau _{\alpha }\in \mathbb{R}$, $\{\mathbf{y}_{\alpha }\}_{\alpha =1}^{m}$ are i.i.d. isotropic…

Let $\a$ be a complex random variable with mean zero and bounded variance $\sigma^{2}$. Let $N_{n}$ be a random matrix of order $n$ with entries being i.i.d. copies of $\a$. Let $\lambda_{1}, ..., \lambda_{n}$ be the eigenvalues of…

Let $\Lambda$ be the limiting smallest eigenvalue in the general (\beta, a)-Laguerre ensemble of random matrix theory. Here \beta>0, a >-1; for \beta=1,2,4 and integer a, this object governs the singular values of certain rank n Gaussian…

In \cite{Diaz} beta type I and II doubly singular distributions were introduced and their densities and the joint densities of nonzero eigenvalues were derived. In such matrix variate distributions $p$, the dimension of two singular Wishart…

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large…

The Laguerre functions $l_{n,\tau}^\alpha$, $n=0,1,\dots$, are constructed from generalized Laguerre polynomials. The functions $l_{n,\tau}^\alpha$ depend on two parameters: scale $\tau>0$ and order of generalization $\alpha>-1$, and form…

We present large deviations principles for the moments of the empirical spectral measure of Wigner matrices and empirical measure of $\beta$-ensembles in three cases : the case of Wigner matrices without Gaussian tails, that is Wigner…

This paper concentrates on asymptotic properties of determinants of some random symmetric matrices. If B_{n,r} is a n x r rectangular matrix and B_{n,r}' its transpose, we study det (B_{n,r}'B_{n,r}) when n,r tends to infinity with r/n \to…

We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general the entries of the upper triangular parts of…

This paper studies the almost sure location of the eigenvalues of matrices ${\bf W}_N {\bf W}_N^{*}$ where ${\bf W}_N = ({\bf W}_N^{(1)T}, ..., {\bf W}_N^{(M)T})^{T}$ is a $ML \times N$ block-line matrix whose block-lines $({\bf…

We studied universality of Wishart ensembles whose covariance matrix has 2 distinct eigenvalues and the number of each of these eigenvalue goes to infinity in the asymptotic limit. In this case, the limiting eigenvalue distribution can be…

For a beta-Jacobi ensemble determined by parameters a_1, a_2 and n, under the restriction that the three parameters go to infinity with n and a_1 being of small orders of a_2, we obtain both the bulk and the edge scaling limits. In…

This work is a companion paper of Gamboa, Nagel, Rouault (J. Funct. Anal. 2016). We continue to explore the connections between large deviations for random objects issued from random matrix theory and sum rules. Here, we are concerned…

We prove universality at the edge of the spectrum for unitary (beta=2), orthogonal (beta=1) and symplectic (beta=4) ensembles of random matrices in the scaling limit for a class of weights w(x)=exp(-V(x)) where V is a polynomial,…

Given a sample $X_0,...,X_{n-1}$ from a $d$-dimensional stationary time series $(X_t)_{t \in \mathbb{Z}}$, the most commonly used estimator for the spectral density matrix $F(\theta)$ at a given frequency $\theta \in [0,2\pi)$ is the…

Random matrix theory successfully models many systems, from the energy levels of heavy nuclei to zeros of $L$-functions. While most ensembles studied have continuous spectral distribution, Burkhardt et al introduced the ensemble of…