Limit theorems in bi-free probability theory

Hasebe, Takahiro; Huang, Hao-Wei; Wang, Jiun-Chau

Limit theorems in bi-free probability theory

Hasebe, Takahiro; Huang, Hao-Wei; Wang, Jiun-Chau

Probability theory and related fields, 2018, 172(3-4), 1081-1119

Permalink : https://hdl.handle.net/2115/76221

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論文情報

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アクセス権	open access
URI	https://hdl.handle.net/2115/76221
タイトル	Limit theorems in bi-free probability theory
著者	Hasebe, Takahiro ; Huang, Hao-Wei ; Wang, Jiun-Chau
e-Rad_Researcher 00633166 著者名 Hasebe, Takahiro
著者名 Huang, Hao-Wei
著者名 Wang, Jiun-Chau
言語	英語
キーワード	Bi-free limit theorem
	Bi-free infinitely divisible distributions
	Bi-freely stable distributions
	Full distributions
	Primary 46L54
	Secondary 60E07
発行日	2018-12
出版者	Springer
収録物名	Probability theory and related fields
巻(号)	172(3-4)
ページ	1081-1119
抄録	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.
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 "Probability Theory and Related Fields". The final authenticated version is available online at: http://dx.doi.org/10.1007/s00440-017-0825-6
PISSN	0178-8051
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.1007/s00440-017-0825-6