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arXiv · 1707.02540

Ona relation between classical and free infinitely divisible transforms

Zbigniew J. Jurek
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Abstract

We study two ways (levels) of finding free-probability analogues of classical infinitely divisible measures. More precisely, we identify their Voiculescu transforms. For free-selfdecomposable measures we found the formula (a differential equation) for their background driving transforms. We illustrate our methods on the hyperbolic characteristic functions. As a by-product our approach may produce new formulas for some definite integrals.

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Zbigniew J. Jurek. 2017-07-09. Ona relation between classical and free infinitely divisible transforms. https://doi.org/10.37190/0208-4147.40.2.9

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