On the law of addition of random matrices: Covariance and the central limit theorem for traces of resolvent

2007 ◽  
pp. 399-416 ◽  
Author(s):  
Leonid Pastur ◽  
V. Vasilchuk
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Matrices ◽  
Central Limit ◽  
The Central Limit Theorem ◽  
The Law

scholarly journals Precise Asymptotics in the Law of the Iterated Logarithm under Sublinear Expectations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mingzhou Xu ◽  
Kun Cheng
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Uniform Convergence ◽  
Central Limit ◽  
Random Variables ◽  
Precise Asymptotics ◽  
Partial Sum ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

By an inequality of partial sum and uniform convergence of the central limit theorem under sublinear expectations, we establish precise asymptotics in the law of the iterated logarithm for independent and identically distributed random variables under sublinear expectations.

scholarly journals On Feller's criterion for the law of the iterated logarithm

1994 ◽  
Vol 17 (2) ◽  
pp. 323-340 ◽  
Author(s):  
Deli Li ◽  
M. Bhaskara Rao ◽  
Xiangchen Wang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Uniform Estimate ◽  
Random Variables ◽  
Independent Random Variables ◽  
Partial Sums ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

Combining Feller's criterion with a non-uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm. Two of these results refine corresponding results of Wittmann (1985) and Egorov (1971). In addition, these results are compared with the corresponding results of Teicher (1974), Tomkins (1983) and Tomkins (1990)

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].

Lognormal genesis

1981 ◽  
Vol 18 (2) ◽  
pp. 542-547 ◽  
Author(s):  
Gavin Brown ◽  
J. W. Sanders
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Lognormal Distribution ◽  
Fundamental Concept ◽  
The Central Limit Theorem ◽  
The Law

Models have been proposed in many diverse areas to generate a lognormal distribution and the underlying idea has always been some form of the law of proportionate effect. In a sense any model must resemble this recipe: take logs and apply the central limit theorem. Our model is no exception. However our formulation is designed to encompass the previous models and demonstrate that the fundamental concept is one of classification. This supersedes a multitude of models which incorporate a mechanism peculiar to a specific application in order to use the law of proportionate effect; we illustrate with applications of the model to ecology, econometrics and geostatistics.

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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