A note on the folklore of free independence

2018/02/03 by Chakrabarty, Arijit, Chakraborty, Sukrit, Hazra, Rajat Subhra
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1802.00952

Abstract

It is shown that a Wishart matrix of standard complex normal random variables is asymptotically freely independent of an independent random matrix, under minimal conditions, in two different sense of asymptotic free independence.

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• Free probability and random matrices
• Strong asymptotic freeness for Wigner and Wishart matrices
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• A combinatorial result on asymptotic independence relations for random matrices with non-commutative entries
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