Basu, Riddhipratim ; Bose, Arup ; Ganguly, Shirshendu ; Hazra, Rajat (2012) Joint convergence of several copies of different patterned random matrices Electronic Journal of Probability, 17 . pp. 1-33. ISSN 1083-6489
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Official URL: http://doi.org/10.1214/EJP.v17-1970
Related URL: http://dx.doi.org/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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Institute of Mathematical Statistics. |
| Keywords: | Free Probability; Hankel Matrix; Joint Convergence; Patterned Matrices; Random Matrices; Reverse Circulant Matrix; Symmetric Circulant Matrix; Toeplitz Matrix; Wigner Matrix. |
| ID Code: | 121058 |
| Deposited On: | 09 Jul 2021 04:42 |
| Last Modified: | 09 Jul 2021 04:42 |
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