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.

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

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

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

scholarly journals Local Semicircle Law and Complete Delocalization for Wigner Random Matrices

2008 ◽  
Vol 287 (2) ◽  
pp. 641-655 ◽  
Author(s):  
László Erdős ◽  
Benjamin Schlein ◽  
Horng-Tzer Yau
Keyword(s):  
Random Matrices ◽  
Semicircle Law ◽  
Local Semicircle Law ◽  
Wigner Random Matrices
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