Bi-monotonic Independence for Pairs of Algebras

Gu, Yinzheng; Hasebe, Takahiro; Skoufranis, Paul

Journal of Theoretical Probability, 2019, 33, 533-566

Permalink : https://hdl.handle.net/2115/80507

このアイテムのアクセス数:348件（2026-08-26 20:14 集計）

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アクセス権	open access
URI	https://hdl.handle.net/2115/80507
タイトル	Bi-monotonic Independence for Pairs of Algebras
著者	Gu, Yinzheng ; Hasebe, Takahiro ; Skoufranis, Paul
著者名 Gu, Yinzheng
e-Rad_Researcher 00633166 著者名 Hasebe, Takahiro
著者名 Skoufranis, Paul
言語	英語
キーワード	Bi-monotonic independence
	Bi-monotonic cumulants
	Bi-monotonic convolution
発行日	2019-02-18
出版者	Springer
収録物名	Journal of Theoretical Probability
巻(号)	33
ページ	533-566
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Accepted Manuscript
権利情報	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.
PISSN	0894-9840
EISSN	1572-9230
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.1007/s10959-019-00884-2