Finite diagonal random matrices

A. Bose, S. Sen

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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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 X_nX^T_n where X_n is a sequence of nonsymmetric r-diagonal random matrices and establish their limiting spectral distribution.
Original languageEnglish
Pages (from-to)819-835
JournalJournal of Theoretical Probability
Volume26
Issue number3
DOIs
Publication statusPublished - 2013
Externally publishedYes

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