scholarly journals Local Semicircle Law Under Fourth Moment Condition

2019 ◽  
Vol 33 (3) ◽  
pp. 1327-1362
Author(s):  
F. Götze ◽  
A. Naumov ◽  
A. Tikhomirov
Keyword(s):  
Moment Condition ◽  
Fourth Moment ◽  
Semicircle Law ◽  
Local Semicircle Law

On Optimal Bounds in the Local Semicircle Law under Four Moment Condition

2019 ◽  
Vol 99 (1) ◽  
pp. 40-43
Author(s):  
F. Götze ◽  
A. A. Naumov ◽  
A. N. Tikhomirov
Keyword(s):  
Moment Condition ◽  
Semicircle Law ◽  
Local Semicircle Law ◽  
Optimal Bounds

scholarly journals On optimal bounds in the local semicircle law under four moment condition

2019 ◽  
Vol 484 (3) ◽  
pp. 265-268
Author(s):  
F. Götze ◽  
A. A. Naumov ◽  
A. N. Tikhomirov
Keyword(s):  
Spectral Distribution ◽  
Moment Condition ◽  
Finite Moment ◽  
Semicircle Law ◽  
Empirical Spectral Distribution ◽  
Local Semicircle Law ◽  
Unit Variance ◽  
Optimal Bounds ◽  
Order Four ◽  
Stieltjes Transforms

We consider symmetric random matrices with independent mean zero and unit variance entries in the upper triangular part. Assuming that the distributions of matrix entries have finite moment of order four, we prove optimal bounds for the distance between the Stieltjes transforms of the empirical spectral distribution function and the semicircle law. Application concerning the convergence rate in probability of the empirical spectral distribution to the semicircle law is discussed as well.

Local semicircle law under weak moment conditions

2016 ◽  
Vol 93 (3) ◽  
pp. 248-250 ◽  
Author(s):  
F. Götze ◽  
A. A. Naumov ◽  
A. N. Tikhomirov ◽  
D. A. Timushev
Keyword(s):  
Moment Conditions ◽  
Semicircle Law ◽  
Local Semicircle Law

An inverse scattering method in time-domain electromagnetics

1981 ◽  
Vol 59 (10) ◽  
pp. 1348-1353
Author(s):  
Sujeet K. Chaudhuri
Keyword(s):  
Inverse Scattering ◽  
Time Domain ◽  
Random Noise ◽  
Power Series Expansion ◽  
Inverse Scattering Method ◽  
Wave Number ◽  
Moment Condition ◽  
Scattering Method ◽  
Fourth Moment ◽  
Rayleigh Coefficient

An inverse scattering model, based on the time-domain concepts of electromagnetic theory is developed. Using the first five (zeroth to fourth) moment condition integrals, the Rayleigh coefficient and the next higher order nonzero coefficient of the power series expansion in k (wave number) of the object backscattering response are recovered. The Rayleigh coefficient and the other coefficient thus recovered are used (with the ellipsoidal assumption for the object shape) to determine the dimensions and orientation of the object.Some numerical results of the application of this coefficient recovery technique to conducting ellipsoidal scatterers are presented. The performance of the software system in the presence of normally distributed random noise is also studied.

scholarly journals Local Semicircle Law in the Bulk for Gaussian β-Ensemble

2012 ◽  
Vol 148 (2) ◽  
pp. 204-232 ◽  
Author(s):  
Philippe Sosoe ◽  
Percy Wong
Keyword(s):  
Semicircle Law ◽  
Local Semicircle Law

scholarly journals Local Semicircle Law for Random Regular Graphs

2017 ◽  
Vol 70 (10) ◽  
pp. 1898-1960 ◽  
Author(s):  
Roland Bauerschmidt ◽  
Antti Knowles ◽  
Horng-Tzer Yau
Keyword(s):  
Regular Graphs ◽  
Semicircle Law ◽  
Local Semicircle Law

Local semicircle law and Gaussian fluctuation for Hermite <italic>β</italic> ensemble

2012 ◽  
Vol 42 (10) ◽  
pp. 1017-1030 ◽  
Author(s):  
ZhiGang BAO ◽  
ZhongGen SU
Keyword(s):  
Semicircle Law ◽  
Local Semicircle Law
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