相关论文: GOE statistics for Anderson models on antitrees an…
We consider products of random matrices that are small, independent identically distributed perturbations of a fixed matrix $T_0$. Focusing on the eigenvalues of $T_0$ of a particular size we obtain a limit to a SDE in a critical scaling.…
It is conjectured that the eigenvalues of random Schrodinger operators at the localization transition in dimensions d>=2 behave like the eigenvalues of the Gaussian Orthogonal Ensemble (GOE). We show that there are sequences of n by m boxes…
For random operators it is conjectured that spectral properties of an infinite-volume operator are related to the distribution of spectral gaps of finite-volume approximations. In particular, localization and pure point spectrum in infinite…
In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of…
We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional…
Probability distribution for the ratio ($r$) of consecutive level spacings of the eigenvalues of a Poisson (generating regular spectra) spectrum and that of a GOE random matrix ensemble are given recently. Going beyond these, for the…
In this work, we study some statistical properties of the extreme eigenstates of the randomly-weighted adjacency matrices of random graphs. We focus on two random graph models: Erd\H{o}s-R\'{e}nyi (ER) graphs and random geometric graphs…
We investigate the nodal count of eigenvectors of random matrices interpreted as operators on signed complete graphs. Our focus is on orthogonally invariant ensembles, with particular attention to the Gaussian Orthogonal Ensemble (GOE). We…
We present a novel approach to study eigenvalues of deformed random matrices. This approach applies to many deformed Gaussian matrix models; two such models are studied in detail: the deformed GOE and the spiked population model.
A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity.…
We study the variance of a linear statistic of the Laplace eigenvalues on a hyperbolic surface, when the surface varies over the moduli space of all surfaces of fixed genus, sampled at random according to the Weil-Petersson measure. The…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…
We investigate the spectral properties of a generalized GOE (Gaussian Orthogonal Ensemble) capable of describing critical statistics. The joint distribution of eigenvalues of this model is expressed as the diagonal element of the density…
As a unifying framework for examining several properties that nominally involve eigenvalues, we present a particular structure of the singular values of the Gaussian orthogonal ensemble (GOE): the even-location singular values are…
This paper details an observation that for more primitive organisms, such as some yeasts, the statistical distribution of the origins of replication sometimes looks remarkably like the distribution of eigenvalues from the Circular…
The generalized Rosenzweig-Porter model with real (GOE) off-diagonal entries arguably constitutes the simplest random matrix ensemble displaying a phase with fractal eigenstates, which we characterize here by using replica methods. We first…
This work is focused on the local eigenvalue statistics for the Anderson tight binding model with non-rank-one perturbations over the canopy tree, at large disorder. On the Hilbert space $\ell^2(\mathcal{C})$, where $ \mathcal{C} $ is the…
We prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operator as the direct sum of half-line Jacobi matrices whose…
We introduce a number of random matrix models describing the Google matrix G of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix diagonalization. We show that for certain models it is…
We present a random matrix interpretation of the distribution functions which have appeared in the study of the one-dimensional polynuclear growth (PNG) model with external sources. It is shown that the distribution, GOE$^2$, which is…