相关论文: Mean left-right eigenvector self-overlap in the re…

It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing…

We study the joint density of eigenvalues for products of independent rectangular real, complex and quaternionic Ginibre matrices. In the limit where the number of matrices tends to infinity, it is shown that the joint probability density…

We investigate eigenvector statistics of the Truncated Unitary ensemble $\mathrm{TUE}(N,M)$ in the weakly non-unitary case $M=1$, that is when only one row and column are removed. We provide an explicit description of generalized overlaps…

In this paper we establish eigenvector delocalization and bulk universality for L\'{e}vy matrices, which are real, symmetric, $N \times N$ random matrices $\textbf{H}$ whose upper triangular entries are independent, identically distributed…

We observe that the distribution of the eigenvalues of an $N$-by-$N$ GUE random matrix is log-concave on $\mathbb{R}^N$, and that the same is true for the law of a single gap between two consecutive eigenvalues. We use this observation to…

We investigate real eigenvalues of real elliptic Ginibre matrices of size $n$, indexed by the parameter of asymmetry $\tau \in [0,1]$. In both the strongly and weakly non-Hermitian regimes, where $\tau \in [0,1)$ is fixed or…

The averages of ratios of characteristic polynomials det(lambda - X) of N x N random matrices X, are investigated in the large N limit for the GUE, GOE and GSE ensemble. The density of states and the two-point correlation function are…

We consider various asymptotic scaling limits $N\to\infty$ for the $2N$ complex eigenvalues of non-Hermitian random matrices in the symmetry class of the symplectic Ginibre ensemble. These are known to be integrable, forming Pfaffian point…

By using the method of orthogonal polynomials we analyze the statistical properties of complex eigenvalues of random matrices describing a crossover from Hermitian matrices characterized by the Wigner- Dyson statistics of real eigenvalues…

Ensembles of complex symmetric, and complex self dual random matrices are known to exhibit local statistical properties distinct from those of the non-Hermitian Ginibre ensembles. On the other hand, in distinction to the latter, the joint…

For an additive perturbation of the complex Ginibre ensemble under a deterministic matrix $X_0$, under certain assumption on $X_0$, we observe that there are only two kinds of local statistical patterns at the spectral edge: GinUE…

We consider large non-Hermitian real or complex random matrices $X$ with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of…

We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue…

The theory of zonal polynomials is used to compute the average of a Schur polynomial of argument $AX$, where $A$ is a fixed matrix and $X$ is from the real Ginibre ensemble. This generalizes a recent result of Sommers and Khorozhenko [J.…

We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree $N$ whose Mahler measure is bounded by a constant. After a change of variables this reduces to a generalization of Ginibre's complex and real…

We study averages of multiplicative eigenvalue statistics in ensembles of orthogonal Haar distributed matrices, which can alternatively be written as Toeplitz+Hankel determinants. We obtain new asymptotics for symbols with Fisher-Hartwig…

We study random, symmetric $N \times N$ band matrices with a band of size $W$ and Bernoulli random variables as entries. This interpolates between nearest neighbour interaction $W = 1$ and Wigner matrices $W = N$. Eigenvectors are known to…

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…

A generalized Wigner matrix perturbed by a finite-rank deterministic matrix is considered. The fluctuations of the largest eigenvalues, which emerge outside the bulk of the spectrum, and the corresponding eigenvectors, are studied. Under…

We consider the ensemble of adjacency matrices of Erd\H{o}s-R\'{e}nyi random graphs, that is, graphs on $N$ vertices where every edge is chosen independently and with probability $p\equiv p(N)$. We rescale the matrix so that its bulk…