Related papers: Optimal decay of eigenvector overlap for non-Hermi…

We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…

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…

We study the overlaps between eigenvectors of nonnormal matrices. They quantify the stability of the spectrum, and characterize the joint eigenvalues increments under Dyson-type dynamics. Well known work by Chalker and Mehlig calculated the…

Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices $A_{n}$ and $B_{n}$ rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix $U_{n}$ (i.e.…

We propose a technique for calculating and understanding the eigenvalue distribution of sums of random matrices from the known distribution of the summands. The exact problem is formidably hard. One extreme approximation to the true density…

We consider the eigenvectors of symmetric matrices with independent heavy tailed entries, such as matrices with entries in the domain of attraction of $\alpha$-stable laws, or adjacencymatrices of Erdos-Renyi graphs. We denote by…

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…

The empirical eigenvalue distribution of the elliptic random matrix ensemble tends to the uniform measure on an ellipse in the complex plane as its dimension tends to infinity. We show this convergence on all mesoscopic scales slightly…

We consider non-Hermitian random matrices $X \in \mathbb{C}^{n \times n}$ with general decaying correlations between their entries. For large $n$, the empirical spectral distribution is well approximated by a deterministic density,…

We consider $N\times N$ Hermitian random band matrices $H=(H_{xy})$, whose entries are centered complex Gaussian random variables. The indices $x,y$ range over the $d$-dimensional discrete torus $(\mathbb Z/L\mathbb Z)^d$ with $d\in…

We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the…

We consider Hermitian and symmetric random band matrices $H$ in $d \geq 1$ dimensions. The matrix elements $H_{xy}$, indexed by $x,y \in \Lambda \subset \Z^d$, are independent and their variances satisfy $\sigma_{xy}^2:=\E \abs{H_{xy}}^2 =…

Classical random matrix ensembles with orthogonal symmetry have the property that the joint distribution of every second eigenvalue is equal to that of a classical random matrix ensemble with symplectic symmetry. These results are shown to…

We investigate the overlap matrix between the eigenvectors of a Wigner matrix $H_{N+K}$ of size $(N+K)\times(N+K)$ and those of its principal minor $H_N$ of size $N\times N$, for both the real symmetric ($\beta=1$) and complex Hermitian…

We prove that with high probability, every eigenvector of a random matrix is delocalized in the sense that any subset of its coordinates carries a non-negligible portion of its $\ell_2$ norm. Our results pertain to a wide class of random…

We consider an ensemble of large non-Hermitian random matrices of the form $\hat{H}+i\hat{A}_s$, where $\hat{H}$ and $\hat{A}_s$ are Hermitian statistically independent random $N\times N$ matrices. We demonstrate the existence of a new…

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…

Consider $N\times N$ symmetric one-dimensional random band matrices with general distribution of the entries and band width $W \geq N^{3/4+\varepsilon}$ for any $\varepsilon>0$. In the bulk of the spectrum and in the large $N$ limit, we…

Let $A$ be an $n\times n$ matrix with mutually independent centered Gaussian entries. Define \begin{align*} \sigma^*:=\max\limits_{i,j\leq n}\sqrt{{\mathbb E}\,|A_{i,j}|^2}, \quad \sigma:=\max\bigg(\max\limits_{j\leq n}\sqrt{{\mathbb…

We study analytically the Chalker-Mehlig mean diagonal overlap $\mathcal{O}(z)$ between left and right eigenvectors associated with a complex eigenvalue $z$ of $N\times N$ matrices in the real Ginibre ensemble (GinOE). We first derive a…