Related papers: Structured perturbations of tridiagonal twisted To…
Given a random sample from a multivariate normal distribution whose covariance matrix is a Toeplitz matrix, we study the largest off-diagonal entry of the sample correlation matrix. Assuming the multivariate normal distribution has the…
We calculate the eigenvalues of a class of random matrices, namely the randomly segmented tridiagonal quasi-Toeplitz (rstq-T) matrix, in exact closed-form. The contexts under which these matrices arise are ubiquitous in physics. In our…
Toeplitz matrices are characterized by their constant diagonals, have been extensively studied in various settings, including over real and complex numbers. However, their study over quaternions is quite sparse. In this paper, we…
We consider the asymptotic behavior of the eigenvalues of Toeplitz matrices with rational symbol as the size of the matrix goes to infinity. Our main result is that the weak limit of the normalized eigenvalue counting measure is a…
In the present paper, we are concerned with the study of the spectral distribution of matrix-sequences showing a non-Hermitian block structure with Toeplitz blocks. We use the notion of geometric mean of matrices and the theory of…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
We study the spectral norm of large rectangular random Toeplitz and circulant matrices with independent entries. For Toeplitz matrices, we show that the scaled norm converges to the norm of a bilinear operator defined via the pointwise…
We study the spectra of $N\times N$ Toeplitz band matrices perturbed by small complex Gaussian random matrices, in the regime $N\gg 1$. We prove a probabilistic Weyl law, which provides an precise asymptotic formula for the number of…
Consider real symmetric, complex Hermitian Toeplitz and real symmetric Hankel band matrix models, where the bandwidth $b_{N}\ra \iy$ but $b_{N}/N \to b$, $b\in [0,1]$ as $N\to \infty$. We prove that the distributions of eigenvalues converge…
We estimate the norms of standard Gaussian random Toeplitz and circulant matrices and their inverses, mostly by means of combining some basic techniques of linear algebra. In the case of circulant matrices we obtain sharp probabilistic…
This is a first paper by the authors dedicated to the distribution of eigenvalues for random perturbations of large bidiagonal Toeplitz matrices.
It is well known that square matrices with independent and identically distributed (iid) random entries are typically well conditioned. A natural question is whether this favorable behavior persists for random matrices whose entries obey…
We investigate the level spacing distribution for three ensembles of real symmetric matrices having additional structural constraint to reduce the number of independent entries to only $ (n+1)/2 $ in contrast to the $ n(n+1)/2 $ for a real…
We investigate the asymptotic behavior of the eigenvalues of spiked perturbations of Wigner matrices when the dimension goes to infinity. The entries of the Hermitian Wigner matrix have a distribution which is symmetric and satisfies a…
It was shown in a series of recent publications that the eigenvalues of $n\times n$ Toeplitz matrices generated by so-called simple-loop symbols admit certain regular asymptotic expansions into negative powers of $n+1$. On the other hand,…
The limiting behavior of the eigenvalues of the Toeplitz matrices $T_{n}[\sigma]=(\hat{\sigma}(i-j))$, where $0\leq i,j \leq n$, as $n \to \infty$, is investigated in the case of complex valued functions $\sigma$ defined on the unit circle…
Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices $A_{n}$ and $B_{n}$ rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix $U_{n}$ (i.e.…
This article deals with the limiting spectral distributions (LSD) of symmetric Toeplitz and Hankel matrices with dependent entries. For any fixed positive integer $m$, we consider these $n \times n$ matrices with entries $\{Y^{(m)}_j /…
This paper is devoted to the asymptotic behavior of all eigenvalues of Symmetric (in general non Hermitian) Toeplitz matrices with moderately smooth symbols which trace out a simple loop on the complex plane line as the dimension of the…
We study the spectrum of large a bi-diagonal Toeplitz matrix subject to a Gaussian random perturbation with a small coupling constant. We obtain a precise asymptotic description of the average density of eigenvalues in the interior of the…