Related papers: Universality for a class of random band matrices
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 prove universality at the edge for rescaled correlation functions of Wigner random matrices in the limit $n\to +\infty$. As a corollary, we show that, after proper rescaling, the 1st, 2nd, 3rd, etc. eigenvalues of Wigner random hermitian…
We consider non-gaussian ensembles of random normal matrices with the constraint that the ensembles are invariant under unitary transformations. We show that the level density of eigenvalues exhibits disk to ring transition in the complex…
We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields…
We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found…
We consider symmetric and Hermitian random matrices whose entries are independent and symmetric random variables with an arbitrary variance pattern. Under a novel Short-to-Long Mixing condition, which is sharp in the sense that it precludes…
A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted…
The universality phenomenon asserts that the distribution of the eigenvalues of random matrix with i.i.d. zero mean, unit variance entries does not depend on the underlying structure of the random entries. For example, a plot of the…
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…
Following E. Wigner's original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix $H$ yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability.…
The momentum spectrum of a periodic network (quantum graph) has a band-gap structure. We investigate the relative density of the bands or, equivalently, the probability that a randomly chosen momentum belongs to the spectrum of the periodic…
This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form $\mathcal{W}_N=\Sigma^{1/2}XX^*\Sigma ^{1/2}$. Here, $X=(x_{ij})_{M,N}$ is an…
We prove that a very general class of $N\times N$ Hermitian random band matrices is in the delocalized phase when the band width $W$ exceeds the critical threshold, $W\gg \sqrt{N}$. In this regime, we show that, in the bulk spectrum, the…
In this paper, we consider the universality of the local eigenvalue statistics of random matrices. Our main result shows that these statistics are determined by the first four moments of the distribution of the entries. As a consequence, we…
I shall present a proof of universality of the microscopic spectral correlations in Verbaarschot's random matrix models of QCD, to corroborate the beautiful agreement between the predictions from the gaussian model and the numerical data.…
We consider the ensemble of adjacency matrices of Erd{\H o}s-R\'enyi random graphs, i.e.\ 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…
We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…
The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…
We obtain the explicit rate of convergence $N^{-1/2 + \epsilon}$ for the gaps of generalized Wigner matrices in the bulk of the spectrum, for distributions of matrix entries possibly atomic and supported on enough points. The proof proceeds…
This paper is a detailed account of the recent progress in understanding the statistical properties of complex eigenvalues of random non-Hermitian matrices reported earlier in our two short communications: Physics Letters A v.226, 46 (1997)…