Central limit theorem and large deviations of the fading Wyner cellular model via product of random matrices theory

2009 ◽  
Vol 45 (1) ◽  
pp. 5-22 ◽  
Author(s):  
N. Levy ◽  
O. Zeitouni ◽  
S. Shamai (Shitz)
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Large Deviations ◽  
Random Matrices ◽  
Central Limit ◽  
Cellular Model ◽  
Product 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].

On the behaviour of a long cascade of linear reservoirs

2000 ◽  
Vol 37 (02) ◽  
pp. 417-428
Author(s):  
John E. Glynn ◽  
Peter W. Glynn
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Large Deviations ◽  
Asymptotic Behaviour ◽  
Central Limit ◽  
Tail Probabilities ◽  
Logarithmic Asymptotics ◽  
Random Fluctuations

This paper describes the limiting asymptotic behaviour of a long cascade of linear reservoirs fed by stationary inflows into the first reservoir. We show that the storage in the nth reservoir becomes asymptotically deterministic as n → ∞, and establish a central limit theorem for the random fluctuations about the deterministic approximation. In addition, we prove a large deviations theorem that provides precise logarithmic asymptotics for the tail probabilities associated with the storage in the nth reservoir when n is large.

On the behaviour of a long cascade of linear reservoirs

2000 ◽  
Vol 37 (2) ◽  
pp. 417-428
Author(s):  
John E. Glynn ◽  
Peter W. Glynn
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Large Deviations ◽  
Asymptotic Behaviour ◽  
Central Limit ◽  
Tail Probabilities ◽  
Logarithmic Asymptotics ◽  
Random Fluctuations

This paper describes the limiting asymptotic behaviour of a long cascade of linear reservoirs fed by stationary inflows into the first reservoir. We show that the storage in the nth reservoir becomes asymptotically deterministic as n → ∞, and establish a central limit theorem for the random fluctuations about the deterministic approximation. In addition, we prove a large deviations theorem that provides precise logarithmic asymptotics for the tail probabilities associated with the storage in the nth reservoir when n is large.

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

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.

Free probability

2018 ◽  
Author(s):  
Alice Guionnet
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Matrices ◽  
Central Limit ◽  
Differential Calculus ◽  
Free Probability ◽  
Integration Theory ◽  
The Central Limit Theorem ◽  
Planar Maps

Free probability was introduced by D. Voiculescu as a theory of noncommutative random variables (similar to integration theory) equipped with a notion of freeness very similar to independence. In fact, it is possible in this framework to define the natural ‘free’ counterpart of the central limit theorem, Gaussian distribution, Brownian motion, stochastic differential calculus, entropy, etc. It also appears as the natural setup for studying large random matrices as their size goes to infinity and hence is central in the study of random matrices as their size go to infinity. In this chapter the free probability framework is introduced, and it is shown how it naturally shows up in the random matrices asymptotics via the so-called ‘asymptotic freeness’. The connection with combinatorics and the enumeration of planar maps, including loop models, are discussed.

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