Year: 2017
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Jurek, Zbigniew J.
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2734331171