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July 2011 Convergence of joint moments for independent random patterned matrices
Arup Bose, Rajat Subhra Hazra, Koushik Saha
Ann. Probab. 39(4): 1607-1620 (July 2011). DOI: 10.1214/10-AOP597

Abstract

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.

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Arup Bose. Rajat Subhra Hazra. Koushik Saha. "Convergence of joint moments for independent random patterned matrices." Ann. Probab. 39 (4) 1607 - 1620, July 2011. https://doi.org/10.1214/10-AOP597

Information

Published: July 2011
First available in Project Euclid: 5 August 2011

zbMATH: 1231.60006
MathSciNet: MR2857252
Digital Object Identifier: 10.1214/10-AOP597

Subjects:
Primary: 60B20
Secondary: 46L53 , 46L54 , 60B10

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

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 4 • July 2011
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