Related papers: Real eigenvalues of elliptic random matrices

The focus of this paper is on the distribution function of the rightmost eigenvalue for the complex elliptic Ginibre ensemble in the limit of weak non-Hermiticity. We show how the limiting distribution function can be expressed in terms of…

Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between…

Let $X$ be a real $(\beta=1)$ or complex $(\beta=2)$ Ginibre ensemble. Let $\{\sigma_i\}_{1\le i\le n}$ be the eigenvalues of $X,$ and $Z_n$ be some rescaled version of $\max_i \Re \sigma_i.$ It was proved that $Z_n$ converges weakly to the…

Quantum physics is generally concerned with real eigenvalues due to the unitarity of time evolution. With the introduction of $\mathcal{PT}$ symmetry, a widely accepted consensus is that, even if the Hamiltonian of the system is not…

We consider the symplectic induced Ginibre process, which is a Pfaffian point process on the plane. Let $N$ be the number of points. We focus on the almost-circular regime where most of the points lie in a thin annulus $\mathcal{S}_{N}$ of…

Given a collection $\{\lambda_1, \dots, \lambda_n\} $ of real numbers, there is a canonical probability distribution on the set of real symmetric or complex Hermitian matrices with eigenvalues $\lambda_1,\ldots,\lambda_n$. In this paper, we…

Let M be an arbitrary Hermitian matrix of order n, and k be a positive integer less than or equal to n. We show that if k is large, the distribution of eigenvalues on the real line is almost the same for almost all principal submatrices of…

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…

We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance $1/n$. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension $n$ goes…

We consider real symmetric and complex Hermitian random matrices with the additional symmetry $h_{xy}=h_{N-x,N-y}$. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble…

We study the distribution of eigenvalues of almost-Hermitian random matrices associated with the classical Gaussian and Laguerre unitary ensembles. In the almost-Hermitian setting, which was pioneered by Fyodorov, Khoruzhenko and Sommers in…

We compute the gap probability that a circle of radius r around the origin contains exactly k complex eigenvalues. Four different ensembles of random matrices are considered: the Ginibre ensembles and their chiral complex counterparts, with…

The Gaussian and Laguerre orthogonal ensembles are fundamental to random matrix theory, and the marginal eigenvalue distributions are basic observable quantities. Notwithstanding a long history, a formulation providing high precision…

We calculate eigenvector statistics in an ensemble of non-Hermitian matrices describing open quantum systems [F. Haake et al., Z. Phys. B 88, 359 (1992)] in the limit of large matrix size. We show that ensemble-averaged eigenvector…

We describe Generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite…

We prove a local law for eigenvalues of the random Hermitian matrices with external source $W_n=\frac{1}{n}X_n+A_n$ where $X_n$ is Wigner matrix and $A_n$ is diagonal matrix with only two values $a, -a$ on the diagonal. The local law is an…

We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test function of…

We suggest a method of studying the joint probability density (JPD) of an eigenvalue and the associated 'non-orthogonality overlap factor' (also known as the 'eigenvalue condition number') of the left and right eigenvectors for…

We consider $n\times n$ real symmetric and hermitian random matrices $H_{n,m}$ equals the sum of a non-random matrix $H_{n}^{(0)}$ matrix and the sum of $m$ rank-one matrices determined by $m$ i.i.d. isotropic random vectors with…

The study of eigenvalue distributions in random matrix theory is often conducted by analyzing the resolvent matrix $ \mathbf{G}_{\mathbf{M}}^N(z) = (z \mathbf{1} - \mathbf{M})^{-1} $. The normalized trace of the resolvent, known as the…