相关论文: A note on switching eigenvalues under small pertur…

We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…

This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…

The leading eigenvalue $\lambda$ of the adjacency matrix of a graph exerts much influence on the behavior of dynamical processes on that graph. It is thus relevant to relate notions of the importance (specifically, centrality measures) of…

One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…

The extreme eigenvalues of adjacency matrices are important indicators on the influences of topological structures to collective dynamical behavior of complex networks. Recent findings on the ensemble averageability of the extreme…

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…

The eigenproblem of low-rank updated matrices are of crucial importance in many applications. Recently, an upper bound on the number of distinct eigenvalues of a perturbed matrix was established. The result can be applied to estimate the…

The goal of this article is to study how much the eigenvalues of large Hermitian random matrices deviate from certain deterministic locations -- or in other words, to investigate optimal rigidity estimates for the eigenvalues. We do this in…

We present two sharp, closed-form empirical Bernstein inequalities for symmetric random matrices with bounded eigenvalues. By sharp, we mean that both inequalities adapt to the unknown variance in a tight manner: the deviation captured by…

We consider the inverse eigenvalue problem for entanglement witnesses, which asks for a characterization of their possible spectra (or equivalently, of the possible spectra resulting from positive linear maps of matrices). We completely…

The detection of the top eigenvalue and its corresponding eigenvector in ensembles of random matrices has significant applications across various fields. An existing method, based on the linear stability of a complementary set of cavity…

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…

Using the superlattice (SL) eigenvalues $E_{\mu ,\nu }^{c,v}$ and eigenfunctions $\varphi_{\mu\nu}^{c,v}(z) $, obtained within the theory of finite periodic systems, where $\mu$ indicates the subbands and $\nu$ the intra-subband levels, we…

It is well-known that the behavior of many dynamical processes running on networks is intimately related to the eigenvalue spectrum of the network. In this paper, we address the problem of inferring global information regarding the…

A standard perturbation result states that perturbed eigenvalues and eigenprojections admit a perturbation series provided that the operator norm of the perturbation is smaller than a constant times the corresponding eigenvalue isolation…

Statistical properties of eigenvectors in non-Hermitian random matrix ensembles are discussed, with an emphasis on correlations between left and right eigenvectors. Two approaches are described. One is an exact calculation for Ginibre's…

The purpose of this note is twofold: firstly to improve the known results on variation of extreme eigenvalues of birth and death matrices and random walk matrices; and secondly to progress towards the solution of a thirty years old open…

For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition…

We propose a working strategy to describe the eigenvalue statistics of random spin systems along the whole phase diagram with thermal to many-body localization (MBL) transition. Our strategy relies on two random matrix (RM) models with…

Pairwise comparisons are used in a wide variety of decision situations where the importance of alternatives should be measured on a numerical scale. One popular method to derive the priorities is based on the right eigenvector of a…