Related papers: Approximating spectral densities of large matrices
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown. We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the…
The spectral density operator $\hat{\rho}(\omega)=\delta(\omega-\hat{H})$ plays a central role in linear response theory as its expectation value, the dynamical response function, can be used to compute scattering cross-sections. In this…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends…
The single-particle spectral function measures the density of electronic states (DOS) in a material as a function of both momentum and energy, providing central insights into phenomena such as superconductivity and Mott insulators. While…
Determining the complexity of molecules has important applications from molecular design to understanding the history of the process that led to the formation of the molecule. Currently, it is not possible to experimentally determine,…
In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
Starting from an independent-particle model with a finite and arbitrary set of single-particle energies, we develop an analytical approximation to the many-body level density $\rho_A(E)$ and to particle-hole densities. We use exact…
We derive a powerful yet simple method for analyzing the local density of states in gapless one dimensional fermionic systems, including extensions such as momentum dependent interaction parameters and hard-wall boundaries. We study the…
We show that an intensity speckle can be directly interpreted as the properties of incident light - amplitude, phase, polarization, and coherency over spatial positions. Revisiting the speckle-correlation scattering matrix (SSM) method [Lee…
Over the last decades, the family of $\alpha$-stale distributions has proven to be useful for modelling in telecommunication systems. Particularly, in the case of radar applications, finding a fast and accurate estimation for the amplitude…
We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these…
Given any fixed $N \times N$ positive semi-definite diagonal matrix $G\ge 0$ we derive the explicit formula for the density of complex eigenvalues for random matrices $A$ of the form $A=U\sqrt{G}$} where the random unitary matrices $U$ are…
We present a theory of linear optical constants based on a single-particle density matrix and implemented in an extension of the real-space multiple scattering code FEFF. This approach avoids the need to compute wave-functions explicitly,…
An algorithm for calculating the spectral intensity of radiation due to the coherent addition of many particles with arbitrary trajectories is described. Direct numerical integration of the Lienard-Wiechert potentials, in the far-field, for…
In hep-th/0111281 the complete set of eigenvectors and eigenvalues of Neumann matrices was found. It was shown also that the spectral density contains a divergent constant piece that being regulated by truncation at level L equals (log…
A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by…