Convergence of joint moments for independent random patterned matrices

Bose, Arup ; Hazra, Rajat Subhra ; Saha, Koushik (2011) Convergence of joint moments for independent random patterned matrices Annals of Probability, 39 (4). pp. 1607-1620. ISSN 0091-1798

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It is known that the joint limit distribution of independent Wigner matrices satisfies a very special asymptotic independence, called freeness. We study the joint convergence of a few other patterned matrices, providing a framework to accommodate other joint laws. In particular, the matricial limits of symmetric circulants and reverse circulants satisfy, respectively, the classical independence and the half independence. The matricial limits of Toeplitz and Hankel matrices do not seem to submit to any easy or explicit independence/dependence notions. Their limits are not independent, free or half independent.

Item Type:Article
Source:Copyright of this article belongs to Institute of Mathematical Statistics.
Keywords:Empirical And Limiting Spectral Distribution; Free Algebras; Half Commutativity; Half Independence; Hankel; Noncommutative Probability; Patterned Matrices; Rayleigh Distribution; Semicircular Law; Symmetric Circulant; Toeplitz And Wigner Matrices.
ID Code:121029
Deposited On:08 Jul 2021 11:45
Last Modified:08 Jul 2021 11:45

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