Central limit theorem for the entries of products of random matrices without the positivity condition

2019 ◽  
Vol 145 ◽  
pp. 254-259
Author(s):  
Ignacio Arbués
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Matrices ◽  
Central Limit ◽  
Products Of Random Matrices ◽  
Positivity Condition

A central limit theorem for normalized products of random matrices

2008 ◽  
Vol 56 (2) ◽  
pp. 183-211
Author(s):  
Rolando Cavazos-Cadena ◽  
Daniel Hernández-Hernández
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Matrices ◽  
Central Limit ◽  
Products Of Random Matrices

On the fluctuations of eigenvalues of multiplicative deformed unitary invariant ensembles

2016 ◽  
Vol 05 (02) ◽  
pp. 1650007 ◽  
Author(s):  
Vladimir Vasilchuk
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Matrices ◽  
Central Limit ◽  
Counting Measure ◽  
Linear Eigenvalue Statistics ◽  
The Central Limit Theorem ◽  
Eigenvalue Statistics ◽  
Leading Term

We consider the ensemble of [Formula: see text] random matrices [Formula: see text], where [Formula: see text] and [Formula: see text] are non-random, unitary, having the limiting Normalized Counting Measure (NCM) of eigenvalues, and [Formula: see text] is unitary, uniformly distributed over [Formula: see text]. We find the leading term of the covariance of traces of resolvent of [Formula: see text] and establish the Central Limit Theorem for sufficiently smooth linear eigenvalue statistics of [Formula: see text] as [Formula: see text].

Central limit theorem of random quadratics forms involving random matrices

2008 ◽  
Vol 78 (6) ◽  
pp. 804-809
Author(s):  
Guangming Pan ◽  
Baiqi Miao ◽  
Baisuo Jin
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Matrices ◽  
Central Limit

scholarly journals CENTRAL LIMIT THEOREM FOR LINEAR STATISTICS OF EIGENVALUES OF BAND RANDOM MATRICES

2013 ◽  
Vol 02 (04) ◽  
pp. 1350009 ◽  
Author(s):  
LINGYUN LI ◽  
ALEXANDER SOSHNIKOV
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Matrices ◽  
Central Limit ◽  
Test Functions ◽  
Linear Statistics ◽  
The Central Limit Theorem ◽  
Linear Statistics Of Eigenvalues

We prove the Central Limit Theorem for linear statistics of the eigenvalues of band random matrices provided [Formula: see text] and test functions are sufficiently smooth.

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