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Bi-monotonic Independence for Pairs of Algebras
| Title: | Bi-monotonic Independence for Pairs of Algebras |
| Authors: | Gu, Yinzheng Browse this author | | Hasebe, Takahiro Browse this author →KAKEN DB | | Skoufranis, Paul Browse this author |
| Keywords: | Bi-monotonic independence | | Bi-monotonic cumulants | | Bi-monotonic convolution |
| Issue Date: | 18-Feb-2019 |
| Journal Title: | Journal of Theoretical Probability |
| Volume: | 33 |
| Start Page: | 533 |
| End Page: | 566 |
| Publisher DOI: | 10.1007/s10959-019-00884-2 |
| Abstract: | In this article, the notion of bi-monotonic independence is introduced as an extension of monotonic independence to the two-faced framework for a family of pairs of algebras in a non-commutative space. The associated cumulants are defined, and a moment-cumulant formula is derived in the bi-monotonic setting. In general, the bi-monotonic product of states is not a state and the bi-monotonic convolution of probability measures on the plane is not a probability measure. This provides an additional example of how positivity need not be preserved under conditional bi-free convolutions. |
| Rights: | This is a post-peer-review, pre-copyedit version of an article published in Journal of Theoretical Probability
. The final authenticated version is available online at: https://doi.org/10.1007/s10959-019-00884-2. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/80507 |
| 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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