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


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.


Download Citation

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.


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

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

Keywords: Free probability , Hankel matrix , joint convergence , patterned matrices , random matrices , Reverse circulant matrix , symmetric circulant matrix , Toeplitz matrix , Wigner matrix


Vol.17 • 2012
Back to Top