Related papers: Toeplitz Inverse Eigenvalue Problem (ToIEP) and Ra…

We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…

Source enumeration typically relies on subspace-based techniques that require accurate separation of signal and noise subspaces. However, prior works do not address coherent sources in small uniform linear arrays, where ambiguities arise in…

We observe a sample of $n$ independent $p$-dimensional Gaussian vectors with Toeplitz covariance matrix $ \Sigma = [\sigma_{|i-j|}]_{1 \leq i,j \leq p}$ and $\sigma_0=1$. We consider the problem of testing the hypothesis that $\Sigma$ is…

Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…

We consider an $N \times N$ random symmetric Toeplitz matrix with an i.i.d. input sequence drawn from a distribution that lies in the domain of attraction of an $\alpha$-stable law for $0 < \alpha < 2$. We show that under an appropriate…

This paper addresses the problem of estimating the Hermitian Toeplitz covariance matrix under practical hardware constraints of sparse observations and coarse quantization. Within the triangular-dithered quantization framework, we propose…

We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with…

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…

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…

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…

Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing…

Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as…

Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral…

Suppose that $T_n$ is a Toeplitz matrix whose entries come from a sequence of independent but not necessarily identically distributed random variables with mean zero. Under some additional tail conditions, we show that the spectral norm of…

Estimating the disturbance or clutter covariance is a centrally important problem in radar space time adaptive processing (STAP). The disturbance covariance matrix should be inferred from training sample observations in practice. Large…

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…

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…

We present a sublinear time algorithm for computing a near optimal low-rank approximation to any positive semidefinite (PSD) Toeplitz matrix $T\in \mathbb{R}^{d\times d}$, given noisy access to its entries. In particular, given entrywise…

Twisted Toeplitz matrices constitute a generalization of Toeplitz matrices in the sense that the entries on each diagonal no longer need to be constant, but are given by the values of a continuous function on a partition of $[0,1]$. We…

Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of positive-definite matrices (here called covariance…