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2012 Joint convergence of several copies of different patterned random matrices
Riddhipratim Basu, Arup Bose, Shirshendu Ganguly, Rajat Hazra
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Electron. J. Probab. 17: 1-33 (2012). DOI: 10.1214/EJP.v17-1970

Abstract

We study the joint convergence of independent copies of several patterned matrices in the non-commutative probability setup. In particular, joint convergence holds for the well known Wigner, Toeplitz, Hankel, Reverse Circulant and Symmetric Circulant matrices. We also study some properties of the limits. In particular, we show that copies of Wigner becomes asymptotically free with copies of any of the above other matrices.

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Riddhipratim Basu. Arup Bose. Shirshendu Ganguly. Rajat Hazra. "Joint convergence of several copies of different patterned random matrices." Electron. J. Probab. 17 1 - 33, 2012. https://doi.org/10.1214/EJP.v17-1970

Information

Accepted: 28 September 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1252.60009
MathSciNet: MR2988397
Digital Object Identifier: 10.1214/EJP.v17-1970

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

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