Related papers: The spectral density of Hardy kernel matrices
We consider a new class of non-self-adjoint matrices that arise from an indefinite self-adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that…
The spectral analysis of the electromagnetic field on the background of a infinitely thin flat plasma layer is carried out. This model is loosely imitating a single base plane from graphite and it is of interest for theoretical studies of…
There are exact solutions to Einstein's equations with negative cosmological constant that represent black holes whose event horizons are manifolds of negative curvature, the so-called topological black holes. Among these solutions there is…
We provide a characterization for the continuous positive definite kernels on $\mathbb R^d$ that are invariant to linear isometries, i.e. invariant under the orthogonal group $O(d)$. Furthermore, we provide necessary and sufficient…
The structure of the spectrum of random operators is studied. It is shown that if the density of states measure of some subsets of the spectrum is zero, then these subsets are empty. In particular follows that absolute continuity of the IDS…
A systematic and easy-to-use method is developed to calculate directly the doubly heavy hadron spectral density in the coordinate space. The correlation function is expressed in terms of hypergeometric functions, and the spectral density is…
In order to clarify the statistical features of complex networks, the spectral density of adjacency matrices has often been investigated. Adopting a static model introduced by Goh, Kahng and Kim, we analyse the spectral density of complex…
We complete the characterization of the possible spectrum of regular ultrafilters D on a set I, where the spectrum is the set of infinite cardinals which are ultraproducts of finite cardinals modulo D.
The spectral density method being applied to the quantum field theory at finite temperature is revived and its possibilities are briefly discussed.
In the paper, a simple condition guaranteing the finiteness property for a bounded set of matrices is presented. Given a bounded set S of real or complex matrices, it is shown that existence of a sequence of matrix products such that the…
In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…
In data science, individual observations are often assumed to come independently from an underlying probability space. Kernel matrices formed from large sets of such observations arise frequently, for example during classification tasks. It…
We define a family of kernels for mixed continuous/discrete hierarchical parameter spaces and show that they are positive definite.
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
We prove a scattering result near certain steady states for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. It is an analogous formulation of the usual Hartree equation…
The problem of computing spectra of operators is arguably one of the most investigated areas of computational mathematics. However, the problem of computing spectra of general bounded infinite matrices has only recently been solved. We…
We consider the scalar anisotropic wave equation. Recently a convergence analysis for radial perfectly matched layers (PML) in the frequency domain was reported and in the present article we continue this approach into the time domain.…
In this paper, we study spectra of first order properties of Erdos-Renyi random graph. We proved that minimal quantifier depth of a formula with an infinite spectrum is either 4 or 5.
We consider bandwidth matrix selection for kernel density estimators (KDEs) of density level sets in $\mathbb{R}^d$, $d \ge 2$. We also consider estimation of highest density regions, which differs from estimating level sets in that one…
A description of the essential spectrum is given for a general class of linear advective PDE with pseudodifferential bounded perturbation. We prove that every point in the Sacker-Sell spectrum of the corresponding bicharacteristic-amplitude…