Bose, Arup ; Sen, Sanchayan (2011) Finite diagonal random matrices Journal of Theoretical Probability . No pp. given.. ISSN 0894-9840
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Official URL: http://www.springerlink.com/content/kl7r8451410380...
Related URL: http://dx.doi.org/10.1007/s10959-011-0378-z
Abstract
The goal of this article is to extend some results of Popescu (Probab. Theory Relat. Fields 144:179, 2009) in several directions. We establish the limiting spectral distribution (LSD) for r-diagonal matrices under reduced moment conditions compared to those required by Popescu. We also deal with the joint convergence of several sequences of such matrices. In particular, we show that there is a large class of such matrices where the joint limit is not free while the marginals are semicircular. We also consider matrices of the form XnXnT where X n is a sequence of nonsymmetric r-diagonal random matrices and establish their limiting spectral distribution.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer. |
| Keywords: | Tridiagonal and Finite Diagonal Matrices; Sample Covariance Type Matrices; Limiting Spectral Distribution; Semicircle Law; Free Independence |
| ID Code: | 93936 |
| Deposited On: | 30 Jun 2012 08:09 |
| Last Modified: | 30 Jun 2012 08:09 |
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