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Related papers: Approximating spectral densities of large matrices

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We give a method for computing asymptotic formulas and approximations for the volumes of spectrahedra, based on the maximum-entropy principle from statistical physics. The method gives an approximate volume formula based on a single convex…

Computational Geometry · Computer Science 2022-11-24 Mahmut Levent Doğan , Jonathan Leake , Mohan Ravichandran

The scattering matrix of the Schrodinger operator with smooth short-range electric and magnetic potentials is considered. The asymptotic density of the eigenvalues of this scattering matrix in the high energy regime is determined. An…

Spectral Theory · Mathematics 2012-08-22 Daniel Bulger , Alexander Pushnitski

The density of state for a complex $N\times N$ random matrix coupled to an external deterministic source is considered for a finite N, and a compact expression in an integral representation is obtained.

Statistical Mechanics · Physics 2009-10-31 S. Hikami , R. Pnini

In the present note we consider a type of matrices stemming in the context of the numerical approximation of distributed order fractional differential equations (FDEs): from one side they could look standard, since they are, real, symmetric…

Numerical Analysis · Mathematics 2021-12-08 M. Bogoya , S. M. Grudsky , S. Serra-Capizzano , C. Tablino-Possio

We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…

Statistical Mechanics · Physics 2009-11-10 S. N. Dorogovtsev , A. V. Goltsev , J. F. F. Mendes , A. N. Samukhin

The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way…

Data Analysis, Statistics and Probability · Physics 2014-07-16 Justin B. Kinney

This paper outlines an approach to the approximation of probability density functions by quadratic forms of weighted orthonormal basis functions with positive semi-definite Hermitian matrices of unit trace. Such matrices are called…

Probability · Mathematics 2016-11-17 Igor G. Vladimirov

We investigate the spectral distribution of large sample covariance matrices with independent columns and entries in the columns that stem from Markov chains. We characterize the limiting spectral densities by their moments.…

Probability · Mathematics 2012-03-19 Olga Friesen , Matthias Löwe

We consider the problem of efficiently computing the Uhlmann fidelity in the case when explicit density matrix descriptions are available. We derive an alternative formula which is simpler to evaluate numerically, saving a factor of 10 in…

Quantum Physics · Physics 2023-01-27 Andrew J. Baldwin , Jonathan A. Jones

We introduce a general, variational scheme applied to Kohn-Sham density functional theory that allows for partitioning of the ground-state density matrix into distinct spectral domains, each of which spanned by an independent diagonal…

Plasma Physics · Physics 2023-08-29 Babak Sadigh , Daniel Aberg , John Pask

Processes with almost periodic covariance functions have spectral mass on lines parallel to the diagonal in the two-dimensional spectral plane. Methods have been given for estimation of spectral mass on the lines of spectral concentration…

Statistics Theory · Mathematics 2008-06-30 Keh-Shin Lii , Murray Rosenblatt

We discuss properties of two methods for ascribing probabilities to the shape of a probability distribution. One is based on the idea of counting the number of modes of a bootstrap version of a standard kernel density estimator. We argue…

Statistics Theory · Mathematics 2007-06-13 Peter Hall , Hong Ooi

The performance of spectral clustering heavily relies on the quality of affinity matrix. A variety of affinity-matrix-construction (AMC) methods have been proposed but they have hyperparameters to determine beforehand, which requires strong…

Machine Learning · Computer Science 2023-02-07 Jicong Fan , Yiheng Tu , Zhao Zhang , Mingbo Zhao , Haijun Zhang

The spectral flux density of stars can indicate their atmospheric physical properties. A detector can obtain any band flux density at the design stage. However, the band flux density is confirmed and fixed in the process of operation…

Instrumentation and Methods for Astrophysics · Physics 2018-09-26 Chuanxin Zhang , Yuan Yuan , Zhaoyang Yu , Fuqiang Wang , Heping Tan

Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances…

Computational Geometry · Computer Science 2014-03-05 Yonathan Aflalo , Anastasia Dubrovina , Ron Kimmel

The present work represents a review for the numerical calculation of the density of states (DoS) for two-dimensional tight-binding models with first neighbors in its normal state and for two superconducting order parameters. One is a…

Superconductivity · Physics 2023-06-16 P. Contreras , A. Devi , D. Uzcategui , E. Ochoa

Ascertaining the physical state of a system is vital in order to understand and predict its behaviour. Tomography is a standard approach used to determine the form of an unknown state. Here we show that an alternative approach, based on…

Quantum Physics · Physics 2013-11-01 Jeff Z. Salvail , Megan Agnew , Allan S. Johnson , Eliot Bolduc , Jonathan Leach , Robert W. Boyd

A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…

Machine Learning · Computer Science 2024-05-01 Fabio A. González , Alejandro Gallego , Santiago Toledo-Cortés , Vladimir Vargas-Calderón

In this technical note, we deal with a spectrum approximation problem arising in THREE-like multivariate spectral estimation approaches. The solution to the problem minimizes a suitable divergence index with respect to an a priori spectral…

Optimization and Control · Mathematics 2014-06-27 Mattia Zorzi

The methods of obtaining the average spectral shape in a low statistics regime are presented. Different approaches to averaging are extensively tested with simulated spectra, based on the ASCA responses. The issue of binning up the spectrum…

Astrophysics · Physics 2009-11-10 Piotr Lubinski