COMBINATORIAL RELATION BETWEEN FREE CUMULANTS AND JACOBI PARAMETERS-Reference-Cited by-同舟云学术

COMBINATORIAL RELATION BETWEEN FREE CUMULANTS AND JACOBI PARAMETERS

Published:2009-06 Issue:02 Volume:12 Page:291-306
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

MŁOTKOWSKI WOJCIECH¹

Affiliation:

1. Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50–384 Wrocław, Poland

Abstract

We find a formula which expresses free and conditionally free cumulants in terms of Jacobi parameters. This leads to some necessary conditions for free and conditionally free infinite divisibility. We also express conditionally free cumulants of two measures in terms of their free cumulants.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025709003653

Reference24 articles.

1. Interacting Fock Spaces and Gaussianization of Probability Measures

2. Positive definite operator sequences

3. Ψ-INDEPENDENT AND SYMMETRIZED WHITE NOISES

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