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Title of Journal: J Stat Phys

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Abbravation: Journal of Statistical Physics

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Springer US

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DOI

10.1007/s11432-013-5021-4

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1572-9613

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On Asymptotic Behavior of Multilinear Eigenvalue S

Authors: A Lytova L Pastur
Publish Date: 2008/11/11
Volume: 133, Issue: 5, Pages: 871-882
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Abstract

We prove the Law of Large Numbers and the Central Limit Theorem for analogs of U and V von Mises statistics of eigenvalues of random matrices as their size tends to infinity We show first that for a certain class of test functions kernels determining the statistics the validity of these limiting laws reduces to the validity of analogous facts for certain linear eigenvalue statistics We then check the conditions of the reduction statements for several most known ensembles of random matrices The reduction phenomenon is well known in statistics dealing with iid random variables It is of interest that an analogous phenomenon is also the case for random matrices whose eigenvalues are strongly dependent even if the entries of matrices are independent

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