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An analogue of the Lévy-Hinčin formula for bi-free infinitely divisible distributions
Yinzheng Gu, Hao-Wei Huang, James A. Mingo · 2015-01-22 · via math.PR updates on arXiv.org

In this paper, we derive the bi-free analogue of the Lévy-Hinčin 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 Lévy-Hinčin representations. Furthermore, we construct the bi-free Lévy processes and the additive bi-free convolution semigroups generated by compactly supported planar probability measures.

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