scholarly journals Large deviations upper bounds and central limit theorems for non-commutative functionals of Gaussian large random matrices

2002 ◽  
Vol 38 (3) ◽  
pp. 341-384 ◽  
Author(s):  
A Guionnet
Keyword(s):  
Large Deviations ◽  
Random Matrices ◽  
Central Limit ◽  
Limit Theorems ◽  
Upper Bounds ◽  
Central Limit Theorems

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

Some probability limit theorems with statistical applications

1953 ◽  
Vol 49 (2) ◽  
pp. 239-246 ◽  
Author(s):  
P. H. Diananda ◽  
M. S. Bartlett
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Upper Bounds ◽  
Central Limit Theorems ◽  
Conditional Distributions ◽  
Probability Limit ◽  
Direct Generalization ◽  
Dependent Variables ◽  
Linear Scalar

In fundamental papers Bernstein (3) and Loève(8) have proved central limit theorems for wide classes of dependent variables. Their theorems are stated in terms of conditional distributions. In the case of dn-dependent variables (see § 3) they assume the existence, as the ‘conditioning’ variates vary, of finite upper bounds for certain conditional absolute moments higher than the second. More recently, Hoeffding and Robbins (7) have proved central limit theorems for m-dependent variables with finite third absolute moments, and Moran(10) has given a direct generalization of the Lindeberg-Lévy theorem for stationary discrete linear scalar processes.

scholarly journals Rates of Convergence in Laplace’s Integrals and Sums and Conditional Central Limit Theorems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 479
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Large Deviations ◽  
Central Limit ◽  
Limit Theorems ◽  
Rates Of Convergence ◽  
Central Limit Theorems ◽  
Error Terms

We obtained the exact estimates for the error terms in Laplace’s integrals and sums implying the corresponding estimates for the related laws of large number and central limit theorems including the large deviations approximation.

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