R--transform associated with asymptotic negative spectral moments of Jacobi ensemble

2013 ◽  
Vol 13 (1) ◽  
pp. 1531-1538
Author(s):  
Jolanta Pielaszkiewicz
Keyword(s):  
Spectral Moments ◽  
Jacobi Ensemble

scholarly journals Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Massimo Gisonni ◽  
Tamara Grava ◽  
Giulio Ruzza
Keyword(s):  
Generating Functions ◽  
Combinatorial Interpretation ◽  
Hurwitz Numbers ◽  
Jacobi Ensemble ◽  
Matrix Ensembles ◽  
Wilson Polynomials ◽  
Unitary Ensemble ◽  
Topological Expansion

AbstractWe express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles. We also provide effective formulæ for generating functions of multipoint correlators of the Jacobi Unitary Ensemble in terms of Wilson polynomials, generalizing the known relations between one point correlators and Wilson polynomials.

GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES

2012 ◽  
Vol 01 (04) ◽  
pp. 1250013 ◽  
Author(s):  
IOANA DUMITRIU ◽  
ELLIOT PAQUETTE
Keyword(s):  
Gaussian Process ◽  
Covariance Matrix ◽  
Law Of Large Numbers ◽  
Test Functions ◽  
Linear Statistics ◽  
Jacobi Ensemble ◽  
Large Numbers ◽  
The Mean ◽  
Shifted Chebyshev Polynomial ◽  
Global Fluctuations

We study the global fluctuations for linear statistics of the form [Formula: see text] as n → ∞, for C1 functions f, and λ1, …, λn being the eigenvalues of a (general) β-Jacobi ensemble. The fluctuation from the mean [Formula: see text] turns out to be given asymptotically by a Gaussian process. We compute the covariance matrix for the process and show that it is diagonalized by a shifted Chebyshev polynomial basis; in addition, we analyze the deviation from the predicted mean for polynomial test functions, and we obtain a law of large numbers.

Multilag Correlation Estimators for Polarimetric Radar Measurements in the Presence of Noise

2012 ◽  
Vol 29 (6) ◽  
pp. 772-795 ◽  
Author(s):  
Lei Lei ◽  
Guifu Zhang ◽  
Richard J. Doviak ◽  
Robert Palmer ◽  
Boon Leng Cheong ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Data Quality ◽  
Signal To Noise Ratio ◽  
Simulated Data ◽  
Radar Data ◽  
Polarimetric Radar ◽  
Signal To Noise ◽  
Spectral Moments ◽  
Radar Measurements

Abstract The quality of polarimetric radar data degrades as the signal-to-noise ratio (SNR) decreases. This substantially limits the usage of collected polarimetric radar data to high SNR regions. To improve data quality at low SNRs, multilag correlation estimators are introduced. The performance of the multilag estimators for spectral moments and polarimetric parameters is examined through a theoretical analysis and by the use of simulated data. The biases and standard deviations of the estimates are calculated and compared with those estimates obtained using the conventional method.

Estimation of rotation and slant angles of a textured plane using spectral moments

2003 ◽  
Vol 34 (6) ◽  
pp. 21-31
Author(s):  
Toshio Tsuji ◽  
Yasuo Yoshida
Keyword(s):  
Spectral Moments

scholarly journals Спектральные моменты характеристик бинарных взаимодействий между линейными молекулами

2021 ◽  
Vol 129 (3) ◽  
pp. 253
Author(s):  
А.В. Соколов ◽  
А.П. Коузов ◽  
Ж.В. Булдырева ◽  
Н.И. Егорова
Keyword(s):  
Interaction Potential ◽  
Spectral Moments ◽  
New Approach ◽  
Relaxation Matrix ◽  
Arbitrary Rank ◽  
Molecular Pair ◽  
Linear Molecules ◽  
Computer Codes ◽  
Spectral Distributions ◽  
The Way

A new approach to derive symmetrized expressions of leading classical moments of spectral distributions characterizing different anisotropic terms of the interaction potential for the case of two liear molecules is presented. The results allow to calculate diffuse shapes formed by transitions between continuous eigenstates of a molecular pair and open the way to account for the nonMarkov effects (due to finite collision durations) in the rotatonal relaxation matrix of an arbitrary rank. The approach is also applied to the spectral moments of vector and tensor characteristics determining the band intensities in the collision-induced spectra of linear molecules. Generally, the use of symmetrized expressions lead to considerably faster computer codes.

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