Related papers: Eigenvector Delocalization for Non-Hermitian Rando…
Building on previous work that provided analytical solutions to generalised matrix eigenvalue problems arising from numerical discretisations, this paper develops exact eigenvalues and eigenvectors for a broader class of $n$-dimensional…
We derive new Hanson-Wright-type inequalities tailored to the quadratic forms of random vectors with sparse independent components. Specifically, we consider cases where the components of the random vector are sparse $\alpha$-subexponential…
Potential disorder in 1D leads to Anderson localization of the entire spectrum. Upon sacrificing hermiticity by adding non-reciprocal hopping, the non-Hermitian skin effect competes with localization. We find another route for…
Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…
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 consider a general class of symmetric or Hermitian random band matrices $H=(h_{xy})_{x,y \in \llbracket 1,N\rrbracket^d}$ in any dimension $d\ge 1$, where the entries are independent, centered random variables with variances…
We consider a closed macroscopic quantum system in a pure state $\psi_t$ evolving unitarily and take for granted that different macro states correspond to mutually orthogonal subspaces $\mathcal{H}_\nu$ (macro spaces) of Hilbert space, each…
We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…
Consider a $n\times n$ sparse non-Hermitian random matrix $X_n$ defined as the Hadamard product between a random matrix with centered independent and identically distributed entries and a sparse Bernoulli matrix with success probability…
Consider a random regular graph of fixed degree $d$ with $n$ vertices. We study spectral properties of the adjacency matrix and of random Schr\"odinger operators on such a graph as $n$ tends to infinity. We prove that the integrated density…
The non-backtracking operator of a graph is a powerful tool in spectral graph theory and random matrix theory. Most existing results for the non-backtracking operator of a random graph concern only eigenvalues or top eigenvectors. In this…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
For a given complex square matrix $A$ with constant row sum, we establish two new eigenvalue inclusion sets. Using these bounds, first we derive bounds for the second largest and smallest eigenvalues of adjacency matrices of $k$-regular…
This paper presents a posteriori error estimates for conforming numerical approximations of eigenvalue clusters of second-order self-adjoint elliptic linear operators with compact resolvent. Given a cluster of eigenvalues, we estimate the…
We consider a random symmetric matrix ${\bf X} = [X_{jk}]_{j,k=1}^n$ with upper triangular entries being independent identically distributed random variables with mean zero and unit variance. We additionally suppose that $\mathbb E…
We consider the eigenvalues and eigenvectors of small rank perturbations of random $N\times N$ matrices. We allow the rank of perturbation $M$ increases with $N$, and the only assumption is $M=o(N)$. In both additive and multiplicative…
We consider random hermitian matrices in which distant above-diagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of eigenvalues by combinatorial methods. We also prove that…
We establish universality of local eigenvalue correlations in unitary random matrix ensembles (1/Z_n) |\det M|^{2\alpha} e^{-n\tr V(M)} dM near the origin of the spectrum. If V is even, and if the recurrence coefficients of the orthogonal…
We present a novel block reduction method for the study of a general class of random band matrices (RBM) defined on the $d$-dimensional lattice $\mathbb{Z}_{L}^d:=\{1,2,\ldots,L\}^{d}$ for $d\in \{1,2\}$, with band width $W$ and an almost…
Euclidean random matrices arise in a wide range of physical systems where interactions are determined by spatial configurations, including disordered media and cooperative phenomena in atomic ensembles. Unlike classical random matrix…