Free-Boolean independence with amalgamation-Reference-Cited by-同舟云学术

Free-Boolean independence with amalgamation

Published:2019-12 Issue:04 Volume:22 Page:1950028
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:

Liu Weihua¹,Zhong Ping²

Affiliation:

1. Department of Mathematics, University of Arizona, 617 N. Santa Rita Ave, Tucson, AZ 85721-0089, USA

2. Department of Mathematics and Statistics, University of Wyoming, Dept. 3036, 1000 E. University Ave, Laramie, WY 82071-3036, USA

Abstract

In this paper, we develop the notion of free-Boolean independence in an amalgamated setting. We construct free-Boolean cumulants and show that the vanishing of mixed free-Boolean cumulants is equivalent to our free-Boolean independence with amalgamation. We also provide a characterization of free-Boolean independence by conditions in terms of mixed moments. In addition, we study free-Boolean independence over a [Formula: see text]-algebra and prove a positivity property. A central limit law for our free-Boolean independence with amalgamation is also studied.

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/S0219025719500280

Reference17 articles.

1. Convolution and limit theorems for conditionally free random variables

2. Combinatorics of Bi-Freeness with Amalgamation

3. Bi-Boolean Independence for Pairs of Algebras

4. Conditionally Bi-Free Independence with Amalgamation

5. Conditionally bi-free independence for pairs of faces