An analogue of the L\'evy-Hincin formula for bi-free infinitely divisible distributions
Abstract
In this paper, we derive the bi-free analogue of the L\'evy-Hincin 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\'evy-Hincin representations. Furthermore, we construct the bi-free L\'evy processes and the additive bi-free convolution semigroups generated by compactly supported planar probability measures.
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