Related papers: Limiting Spectral Measures for Random Matrix Ensem…
In this article we show the existence of limiting spectral distribution of a symmetric random matrix whose entries come from a stationary Gaussian process with covariances satisfying a summability condition. We provide an explicit…
In this article we investigate high-dimensional banded sample covariance matrices under the regime that the sample size $n$, the dimension $p$ and the bandwidth $d$ tend simultaneously to infinity such that $$n/p\to 0 \ \ \text{and} \ \…
This article is concerned with the spectral behavior of $p$-dimensional linear processes in the moderately high-dimensional case when both dimensionality $p$ and sample size $n$ tend to infinity so that $p/n\to0$. It is shown that, under an…
Consider a square random matrix with independent and identically distributed entries of mean zero and unit variance. We show that as the dimension tends to infinity, the spectral radius is equivalent to the square root of the dimension in…
In this paper we consider a new normalization of matrices obtained by choosing distinct codewords at random from linear codes over finite fields and find that under some natural algebraic conditions of the codes their empirical spectral…
We consider the empirical eigenvalue distribution of an $m\times m$ principle submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. Earlier work of Petz and R\'effy identified the limiting spectral measure…
We consider an ensemble of nxn real symmetric random matrices A whose entries are determined by independent identically distributed random variables that have symmetric probability distribution. Assuming that the moment 12+2delta of these…
We consider banded block Toeplitz matrices $T_n$ with $n$ block rows and columns. We show that under certain technical assumptions, the normalized eigenvalue counting measure of $T_n$ for $n\to\infty$ weakly converges to one component of…
It is known that the generating function $f$ of a sequence of Toeplitz matrices $\{T_n(f)\}_n$ may not describe the asymptotic distribution of the eigenvalues of $T_n(f)$ if $f$ is not real. In a recent paper, we assume as a working…
We study the normalized eigenvalue counting measure d\sigma of matrices of long-range percolation model. These are (2n+1)\times (2n+1) random real symmetric matrices H=\{H(i,j)\}_{i,j} whose elements are independent random variables taking…
We study the limiting spectral measure of large random Helson matrices and large random matrices of certain patterned structures. Given a real random variable $X \in L^{2+ \varepsilon}(\mathbb{P}) $ for some $\varepsilon > 0$ and…
We introduce a new family of $N\times N$ random real symmetric matrix ensembles, the $k$-checkerboard matrices, whose limiting spectral measure has two components which can be determined explicitly. All but $k$ eigenvalues are in the bulk,…
Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Bordered and framed Toeplitz/Hankel determinants have the same structure as Toeplitz/Hankel determinants except in small number of matrix rows and/or columns. We review these structured determinants and their connections to orthogonal…
Our goal is to study statistical properies of "dielectric resonances" which are poles of conductance of a large random $LC$ network. Such poles are a particular example of eigenvalues $\lambda_n$ of matrix pencils ${\bf H}-\lambda {\bf W}$,…
We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices : any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the…
We study the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows one of the Ewens measures on the symmetric group. If we apply a smooth enough…
Patterned random matrices such as the reverse circulant, the symmetric circulant, the Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD), have attracted much attention. Under the assumption that the…
Spectral statistics of hermitian random Toeplitz matrices with independent identically distributed elements is investigated numerically. It is found that the eigenvalue statistics of complex Toeplitz matrices is surprisingly well…