On the variance of linear statistics of Hermitian random matrices
Min C.; Chen Y.
Source PublicationActa Physica Polonica B
AbstractLinear statistics, a random variable built out of the sum of the evaluation of functions at the eigenvalues of a N ×N random matrix, Σ f(x) or tr f(M), is an ubiquitous statistical characteristics in random matrix theory. Hermitian random matrix ensembles, under the eigenvalue-eigenvector decompositions give rise to the joint probability density functions of N random variables. We show that if f(·) is a polynomial of degree K, then the variance of tr f(M) is of the form of Σ n(d) and d is related to the expansion coefficients c of the polynomial f(x) = Σ c P(x), where P(x) are polynomials of degree n, orthogonal with respect to the weights [equation presented here], (0 < a < x < b < 1), respectively.
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
AffiliationUniversidade de Macau
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GB/T 7714
Min C.,Chen Y.. On the variance of linear statistics of Hermitian random matrices[J]. Acta Physica Polonica B,2016,47(4):1127-1146.
APA Min C.,&Chen Y..(2016).On the variance of linear statistics of Hermitian random matrices.Acta Physica Polonica B,47(4),1127-1146.
MLA Min C.,et al."On the variance of linear statistics of Hermitian random matrices".Acta Physica Polonica B 47.4(2016):1127-1146.
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