Related papers: Computing marginal eigenvalue distributions for th…
It is well known that Pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices. Moreover the parametric correlations in the crossover to complex random matrices are evaluated in the…
We derive Painlev\'e--type expressions for the distribution of the $m^{th}$ largest eigenvalue in the Gaussian Orthogonal and Symplectic Ensembles in the edge scaling limit. The work of Johnstone and Soshnikov (see [7], [10]) implies the…
We examine the asymptotics of the moments of characteristic polynomials of $N\times N$ matrices drawn from the Hermitian ensembles of Random Matrix Theory, in the limit as $N\to\infty$. We focus in particular on the Gaussian Unitary…
Consider the $n\times n$ matrix $X_n=A_n+H_n$, where $A_n$ is a $n\times n$ matrix (either deterministic or random) and $H_n$ is a $n\times n$ matrix independent from $A_n$ drawn from complex Ginibre ensemble. We study the limiting…
Let $G, G_1,\dots,G_N$ be independent copies of a standard gaussian random vector in $\mathbb{R}^d$ and denote by $\Gamma = \sum_{i=1}^N \langle G_i,\cdot\rangle e_i$ the standard gaussian ensemble. We show that, for any set $A\subset…
Complex Hermitian random matrices with a unitary symmetry can be distinguished by a weight function. When this is even, it is a known result that the distribution of the singular values can be decomposed as the superposition of two…
We consider $N\times N$ Hermitian or symmetric random matrices with independent entries. The distribution of the $(i,j)$-th matrix element is given by a probability measure $\nu_{ij}$ whose first two moments coincide with those of the…
Correlation function of complex eigenvalues of N by N random matrices drawn from non-Hermitean random matrix ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are…
A family of random matrix ensembles interpolating between the GUE and the Ginibre ensemble of $n\times n$ matrices with iid centered complex Gaussian entries is considered. The asymptotic spectral distribution in these models is uniform in…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
We study the distribution of the eigenvalue condition numbers $\kappa_i=\sqrt{ (\mathbf{l}_i^* \mathbf{l}_i)(\mathbf{r}_i^* \mathbf{r}_i)}$ associated with real eigenvalues $\lambda_i$ of partially asymmetric $N\times N$ random matrices…
The $\beta$ ensembles are a class of eigenvalue probability densities which generalise the invariant ensembles of classical random matrix theory. In the case of the Gaussian and Laguerre weights, the corresponding eigenvalue densities are…
Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we…
In this review we summarise recent results for the complex eigenvalues and singular values of finite products of finite size random matrices, their correlation functions and asymptotic limits. The matrices in the product are taken from…
We compute individual distributions of low-lying eigenvalues of massive chiral random matrix ensembles by the Nystr\"om-type quadrature method for evaluating the Fredholm determinant and Pfaffian that represent the analytic continuation of…
Consider a $N\times n$ matrix $\Sigma_n=\frac{1}{\sqrt{n}}R_n^{1/2}X_n$, where $R_n$ is a nonnegative definite Hermitian matrix and $X_n$ is a random matrix with i.i.d. real or complex standardized entries. The fluctuations of the linear…
It is well known that Gaussian symplectic ensemble (GSE) is defined on the space of $n\times n$ quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices. As a…
This paper studies the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices and matrices from the Gaussian unitary ensemble. In particular, the kth…
The goal of this article is to study how much the eigenvalues of large Hermitian random matrices deviate from certain deterministic locations -- or in other words, to investigate optimal rigidity estimates for the eigenvalues. We do this in…
We compute individual distributions of low-lying eigenvalues of a chiral random matrix ensemble interpolating symplectic and unitary symmetry classes by the Nystr\"om-type method of evaluating the Fredholm Pfaffian and resolvents of the…