On a class of free Levy laws related to a regression problem

Details On a class of free Levy laws related to a regression problem On a class of free Levy laws related to a regression problem

2004-10-28

arxiv.org/abs/math/0410601v3

Journal of Functional Analysis Volume 236 (2006), Pages 59-77

Mathematics

Operator Algebras

LaTeX, v2: strengthened main theorem

Scientific paper

10.1016/j.jfa.2005.09.010

The free Meixner laws arise as the distributions of orthogonal polynomials with constant-coefficient recursions. We show that these are the laws of the free pairs of random variables which have linear regressions and quadratic conditional variances when conditioned with respect to their sum. We apply this result to describe free Levy processes with quadratic conditional variances, and to prove a converse implication related to asymptotic freeness of random Wishart matrices.

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