Related papers: On eigenvector statistics in the spherical and tru…
We consider pairs of GOE (Gaussian Orthogonal Ensemble) matrices which are correlated with each others, and subject to additive and multiplicative rank-one perturbations. We focus on the regime of parameters in which the finite-rank…
We investigate the distribution of eigenvalues of weighted adjacency matrices from a specific ensemble of random graphs. We distribute $N$ vertices across a fixed number $\kappa$ of components, with asymptotically $\alpha_j \dot N$ vertices…
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 consider the singular vectors of any $m \times n$ submatrix of a rectangular $M \times N$ Gaussian matrix and study their asymptotic overlaps with those of the full matrix, in the macroscopic regime where $N \,/\, M\,$, $m \,/\, M$ as…
We consider the empirical eigenvalue distribution of an $m\times m$ principal submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. For $n$ and $m$ large with $\frac{m}{n}=\alpha$, the empirical spectral…
We compute exactly the overlap between the eigenvectors of two large empirical covariance matrices computed over intersecting time intervals, generalizing the results obtained previously for non-intersecting intervals. Our method relies on…
We study eigenvectors in the deformed Gaussian unitary ensemble of random matrices $H=W\tilde{H}W$, where $\tilde{H}$ is a random matrix from Gaussian unitary ensemble and $W$ is a deterministic diagonal matrix with positive entries. Using…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…
The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite rank random matrices is found in terms of a Painlev\'e V system, and the solution of its associated linear isomonodromic system. In…
Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products of…
This paper is concerned with the explicit computation of the limiting distribution function of the largest real eigenvalue in the real Ginibre ensemble when each real eigenvalue has been removed independently with constant likelihood. We…
The paper proves several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices. It is shown that the covariance of the limiting multivariate Gaussian distribution is diagonalized by choosing…
Consider the product of $m$ independent $n\times n$ random matrices from the spherical ensemble for $m\ge 1$. The empirical distribution based on the $n$ eigenvalues of the product is called the empirical spectral distribution. Two recent…
We show that some of the best-known matrix decompositions of some of the best-known random matrix ensembles give us the unique $G$-invariant uniform distributions on some of the best-known manifolds. The eigenvectors distributions of the…
This paper is concerned with complex eigenvalues of truncated unitary quaternion matrices equipped with the Haar measure. The joint eigenvalue probability density function is obtained for truncations of any size. We also obtain the spectral…
Statistical properties of non--symmetric real random matrices of size $M$, obtained as truncations of random orthogonal $N\times N$ matrices are investigated. We derive an exact formula for the density of eigenvalues which consists of two…
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…
The model of heavy Wigner matrices generalizes the classical ensemble of Wigner matrices: the sub-diagonal entries are independent, identically distributed along to and out of the diagonal, and the moments its entries are of order 1/N,…
Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of…