Finite Diagonal Random Matrices

Arup Bose and Sanchayan Sen ()
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Sanchayan Sen: Courant Institute of Mathematical Sciences

Journal of Theoretical Probability, 2013, vol. 26, issue 3, 819-835

Abstract: 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 $X_{n}X_{n}^{T}$ where X n is a sequence of nonsymmetric r-diagonal random matrices and establish their limiting spectral distribution.

Keywords: Tridiagonal and finite diagonal matrices; Sample covariance type matrices; Limiting spectral distribution; Semicircle law; Free independence; 60B20; 60B10; 46L53; 46L54 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-011-0378-z

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