Matricially free random variables

Details Matricially free random variables Matricially free random variables

2008-12-02

arxiv.org/abs/0812.0488v1

J. Funct. Anal., Vol. 258 (2010), 4075-4121

Mathematics

Operator Algebras

38 pages, 4 figures

Scientific paper

10.1016/j.jfa.2010.03.010

We show that the operatorial framework developed by Voiculescu for free random variables can be extended to arrays of random variables whose multiplication imitates matricial multiplication. The associated notion of independence, called matricial freeness, can be viewed as a generalization of both freeness and monotone independence. At the same time, the sums of matricially free random variables, called random pseudomatrices, are closely related to Gaussian random matrices. The main results presented in this paper concern the standard and tracial central limit theorems for random pseudomatrices and the corresponding limit distributions which can be viewed as matricial generalizations of semicirle laws.

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