An analogue of the L\'{e}vy-Hin\v{c}in formula for bi-free infinitely divisible distributions

Autor:	Gu, Yinzheng, Huang, Hao-Wei, Mingo, James A.
Rok vydání:	2015
Předmět:	Mathematics - Operator Algebras Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	In this paper, we derive the bi-free analogue of the L\'{e}vy-Hin\v{c}in formula for compactly supported planar probability measures which are infinitely divisible with respect to the additive bi-free convolution introduced by Voiculescu. We also provide examples of bi-free infinitely divisible distributions with their bi-free L\'{e}vy-Hin\v{c}in representations. Furthermore, we construct the bi-free L\'{e}vy processes and the additive bi-free convolution semigroups generated by compactly supported planar probability measures. Comment: Typos fixed and modifications made
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1501.05369 Zobrazit plný text záznamu View this record from Arxiv