Ona relation between classical and free infinitely divisible transforms
Probability
2022-08-02 v1
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.
Cite
@article{arxiv.1707.02540,
title = {Ona relation between classical and free infinitely divisible transforms},
author = {Zbigniew J. Jurek},
journal= {arXiv preprint arXiv:1707.02540},
year = {2022}
}