Related papers: Tridiagonal random matrices, an analytic approach

Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products of…

This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…

This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the…

We consider $N\times N$ symmetric or hermitian random matrices with independent, identically distributed entries where the probability distribution for each matrix element is given by a measure $\nu$ with a subexponential decay. We prove…

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 show that the distribution of (a suitable rescaling of) a single eigenvalue gap $\lambda_{i+1}(M_n)-\lambda_i(M_n)$ of a random Wigner matrix ensemble in the bulk is asymptotically given by the Gaudin-Mehta distribution, if the Wigner…

The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…

Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the…

Let $W_n= \frac{1}{\sqrt n} M_n$ be a Wigner matrix whose entries have vanishing third moment, normalized so that the spectrum is concentrated in the interval $[-2,2]$. We prove a concentration bound for $N_I = N_I(W_n)$, the number of…

In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…

We explore the limiting empirical eigenvalue distributions arising from matrices of the form \[A_{n+1} = \begin{bmatrix} A_n & I\\ I & A_n \end{bmatrix} , \]where $A_0$ is the adjacency matrix of a $k$-regular graph. We find that for…

We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in…

We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…

In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue…

This article focuses on linear eigenvalue statistics of Hankel matrices with independent entries. Using the convergence of moments we show that the linear eigenvalue statistics of Hankel matrices for odd degree monomials with degree greater…

We develop techniques to compute the k-th Moment of the Eigenvalue-statistic for a random Matrix M the entries of which do not have to be necessarily Independent. The dependence is controlled via an equivalence relation on the pairs of the…

Let $\a$ be a real-valued random variable of mean zero and variance 1. Let $M_n(\a)$ denote the $n \times n$ random matrix whose entries are iid copies of $\a$ and $\sigma_n(M_n(\a))$ denote the least singular value of $M_n(\a)$.…

McKay proved that the limiting spectral measures of the ensembles of $d$-regular graphs with $N$ vertices converge to Kesten's measure as $N\to\infty$. In this paper we explore the case of weighted graphs. More precisely, given a large…

We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…

We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and appropriate projections of the corresponding eigenvectors of…