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Limit theorems in bi-free probability theory
| Title: | Limit theorems in bi-free probability theory |
| Authors: | Hasebe, Takahiro Browse this author →KAKEN DB | | Huang, Hao-Wei Browse this author | | Wang, Jiun-Chau Browse this author |
| Keywords: | Bi-free limit theorem | | Bi-free infinitely divisible distributions | | Bi-freely stable distributions | | Full distributions | | Primary 46L54 | | Secondary 60E07 |
| Issue Date: | Dec-2018 |
| Publisher: | Springer |
| Journal Title: | Probability theory and related fields |
| Volume: | 172 |
| Issue: | 3-4 |
| Start Page: | 1081 |
| End Page: | 1119 |
| Publisher DOI: | 10.1007/s00440-017-0825-6 |
| Abstract: | In this paper additive bi-free convolution is defined for general Borel probability measures, and the limiting distributions for sums of bi-free pairs of self-adjoint commuting random variables in an infinitesimal triangular array are determined. These distributions are characterized by their bi-freely infinite divisibility, and moreover, a transfer principle is established for limit theorems in classical probability theory and Voiculescu's bi-free probability theory. Complete descriptions of bi-free stability are given and fullness of planar probability distributions is studied. All these results reveal one important feature about the theory of bi-free probability that it parallels the classical theory perfectly well. The emphasis in the whole work is not on the tool of bi-free combinatorics but only on the analytic machinery. |
| Rights: | This is a post-peer-review, pre-copyedit version of an article published in "Probability Theory and Related Fields". The final authenticated version is available online at: http://dx.doi.org/10.1007/s00440-017-0825-6 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/76221 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 長谷部 高広
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