On a class of free Lévy laws related to a regression problem
By M. Bożejko, Wlodzimierz Bryc. 2004
138 citations recorded by the source corpus.
Abstract 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.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/22cbcad7fe323da874a3fb28ea42f0d3cae780bb
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In Mathematical Physics
- Alain Rouault
- Ion Nechita
- Karol Zyczkowski
- Benoît Collins
- Roland Speicher
- T. Banica
- Michel Ledoux
- Stephen J. Curran
In Statistics and Probability
- Ion Nechita
- Benoît Collins
- Alain Rouault
- Karol A. Penson
- Karol Zyczkowski
- Roland Speicher
- Michel Ledoux
- T. Banica
Citations in the corpus
- Generating random density matrices (2010, background): “The measure (10) can be connected to the free Meixner measures of [23]: νk is the free Meixner measure of parameters a = 0 and b = −1/k.”
- Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles (2006, background): “Itcould also be seen starting from the above form ulae using dilatationsand free convolutionsand com paring with form ula (7)page6 in Bozejko and Bryc(2005).”
- Askey--Wilson polynomials, quadratic harnesses and martingales (2008, unknown): “1) appears in [7], (3), with their a = θ √ t and their b = τ t .”