Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896751 | Journal of Functional Analysis | 2018 | 39 Pages |
Abstract
We develop an analytic machinery to study Voiculescu's bi-free partial S-transform and then use the results to characterize the multiplicative bi-free infinite divisibility. It is shown that the class of infinitely divisible distributions coincides with the class of limit distributions for products of bi-free pairs of left and right infinitesimal unitaries, where the pairs are not required to be identically distributed but all left variables are assumed to commute with all right variables. Furthermore, necessary and sufficient conditions for convergence to a given infinitely divisible distribution are found.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Hao-Wei Huang, Jiun-Chau Wang,