scholarly journals Distribution of linear statistics of singular values of the product of random matrices

Bernoulli ◽  
2017 ◽  
Vol 23 (4B) ◽  
pp. 3067-3113
Author(s):  
Friedrich Götze ◽  
Alexey Naumov ◽  
Alexander Tikhomirov
Keyword(s):  
Random Matrices ◽  
Singular Values ◽  
Linear Statistics ◽  
Product Of Random Matrices

scholarly journals Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

2014 ◽  
Vol 329 (2) ◽  
pp. 641-686 ◽  
Author(s):  
Florent Benaych-Georges ◽  
Alice Guionnet ◽  
Camille Male
Keyword(s):  
Random Matrices ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Linear Statistics ◽  
Heavy Tailed

Lyapunov indices of a product of random matrices

1989 ◽  
Vol 44 (5) ◽  
pp. 11-71 ◽  
Author(s):  
I Ya Gol'dsheid ◽  
G A Margulis
Keyword(s):  
Random Matrices ◽  
Product Of Random Matrices

Pair dependent linear statistics for CβE

2020 ◽  
pp. 2150035
Author(s):  
Ander Aguirre ◽  
Alexander Soshnikov ◽  
Joshua Sumpter
Keyword(s):  
Zeta Function ◽  
Random Matrices ◽  
Riemann Zeta Function ◽  
Classical Result ◽  
Pair Correlation ◽  
Test Function ◽  
Linear Statistics ◽  
Smooth Test ◽  
Riemann Zeta ◽  
Counting Statistics

We study the limiting distribution of a pair counting statistics of the form [Formula: see text] for the circular [Formula: see text]-ensemble (C[Formula: see text]E) of random matrices for sufficiently smooth test function [Formula: see text] and [Formula: see text] For [Formula: see text] and [Formula: see text] our results are inspired by a classical result of Montgomery on pair correlation of zeros of Riemann zeta function.

scholarly journals On the Asymptotic Distribution of Singular Values of Powers of Random Matrices

2014 ◽  
Vol 199 (2) ◽  
pp. 68-87
Author(s):  
N. V. Alexeev ◽  
F. Götze ◽  
A. N. Tikhomirov
Keyword(s):  
Asymptotic Distribution ◽  
Random Matrices ◽  
Singular Values
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