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

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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.
LaTeX, v2: strengthened main theorem

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Operator Algebras, Probability, 46L53

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http://salesiana.dossiersoluciones.com/handle/123456789/100921

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0410601
 http://arxiv.org/abs/math/0410601
 Journal of Functional Analysis Volume 236 (2006), Pages 59-77
 doi:10.1016/j.jfa.2005.09.010

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arXiv