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arXiv · 1501.05369

An analogue of the Lévy-Hinčin formula for bi-free infinitely divisible distributions

Yinzheng Gu·Hao-Wei Huang·James A. Mingo
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Abstract

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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Yinzheng Gu, Hao-Wei Huang, James A. Mingo. 2015-07-09. An analogue of the Lévy-Hinčin formula for bi-free infinitely divisible distributions. https://arxiv.org/abs/1501.05369

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