Diffusion onGL(N,C)/U(N)and Eigenvalue Density forN→∞Limit

1998 ◽  
Vol 67 (2) ◽  
pp. 421-425
Author(s):  
Toshinao Akuzawa ◽  
Miki Wadati
Keyword(s):  
Eigenvalue Density

scholarly journals Eigenvalue density of the doubly correlated Wishart model: exact results

2015 ◽  
Vol 48 (17) ◽  
pp. 175204 ◽  
Author(s):  
Daniel Waltner ◽  
Tim Wirtz ◽  
Thomas Guhr
Keyword(s):  
Exact Results ◽  
Eigenvalue Density

scholarly journals On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Lung-Hui Chen
Keyword(s):  
Density Function ◽  
Functional Derivative ◽  
Index Of Refraction ◽  
Velocity Variation ◽  
Transmission Spectra ◽  
Motion Velocity ◽  
Translation Invariant ◽  
Eigenvalue Density ◽  
Position Variable ◽  
Invariant Properties

We study the translation invariant properties of the eigenvalues of scattering transmission problem. We examine the functional derivative of the eigenvalue density function Δ(x^) to the defining index of refraction n(x). By the limit behaviors in frequency sphere, we prove some results on the inverse uniqueness of index of refraction. In physics, Doppler’s effect connects the variation of the frequency/eigenvalue and the motion velocity/variation of position variable. In this paper, we proved the functional derivative ∂rΔx^=(1+nrx^)/π.

scholarly journals On the shape of the ground state eigenvalue density of a random Hill's equation

2006 ◽  
Vol 59 (7) ◽  
pp. 935-976 ◽  
Author(s):  
Santiago Cambronero ◽  
Brian Rider ◽  
José Ramírez
Keyword(s):  
Ground State ◽  
Hill’S Equation ◽  
Eigenvalue Density ◽  
Hill's Equation

SPECTRAL DISTRIBUTION ANALYSIS OF RANDOM INTERACTIONS WITH J-SYMMETRY AND ITS EXTENSIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 318-333 ◽  
Author(s):  
V. K. B. KOTA ◽  
MANAN VYAS ◽  
K. B. K. MAYYA
Keyword(s):  
Spectral Distribution ◽  
Distribution Theory ◽  
Distribution Analysis ◽  
Regular Feature ◽  
Gaussian Form ◽  
Random Interactions ◽  
Eigenvalue Density ◽  
Regular Structures ◽  
Cross Correlations ◽  
Propagation Methods

Spectral distribution theory, based on average-fluctuation separation and trace propagation, is applied in the analysis of some properties of a system of m (identical) nucleons in shell model j-orbits with random interactions preserving angular momentum J-symmetry. Employing the bivariate Gaussian form with Edgeworth corrections for fixed E (energy) and M (Jz eigenvalue) density of states ρ(E,M), analytical results, in the form of expansions to order [J(J+1)]2, are derived for energy centroids Ec(m,J) and spectral variances σ2(m,J). They are used to study distribution of spectral widths, J=0 preponderance in energy centroids, lower order cross correlations in states with different J's and so on. Also, an expansion is obtained for occupation probabilities over spaces with fixed M. All the results obtained with spectral distribution theory compare well with those obtained recently using quite different methods. In addition, using trace propagation methods, a regular feature, that they are nearly constant, of spectral variances generated by random interactions is demonstrated using several examples. These open a new window to study regular structures generated by random interactions.

Asymptotic Eigenvalue Density of Noise Covariance Matrices

2012 ◽  
Vol 60 (7) ◽  
pp. 3415-3424 ◽  
Author(s):  
Ravishankar Menon ◽  
Peter Gerstoft ◽  
William S. Hodgkiss
Keyword(s):  
Covariance Matrices ◽  
Eigenvalue Density ◽  
Asymptotic Eigenvalue ◽  
Noise Covariance
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