Joint convergence of several copies of different patterned random matrices

2011/08/20 by Basu, Riddhipratim, Bose, Arup, Ganguly, Shirshendu +1
#46L53 #46L54 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 60B20 #Probability (math.PR) #Secondary 60B10

paper · doi:10.48550/arxiv.1108.4099

Abstract

We study the joint convergence of independent copies of several patterned matrices in the noncommutative 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.

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