We study deformations of the free convolution arising via invertible transformations of probability measures on the real line T:μ ↦ Tμ. We define new associative convolutions of measures by . We discuss infinite divisibility with respect to these convolutions, and we establish a Lévy-Khintchine formula. We conclude the paper by proving that for any such deformation of free probability all probability measures μ have the Nica-Speicher property, that is, one can find their convolution power for all s ≥ 1. This behaviour is similar to the free case, as in the original paper of Nica and Speicher [NS].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-23,
author = {\L ukasz Jan Wojakowski},
title = {The L\'evy-Khintchine formula and Nica-Speicher property for deformations of the free convolution},
journal = {Banach Center Publications},
volume = {75},
year = {2007},
pages = {309-314},
zbl = {1140.46327},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-23}
}
Łukasz Jan Wojakowski. The Lévy-Khintchine formula and Nica-Speicher property for deformations of the free convolution. Banach Center Publications, Tome 75 (2007) pp. 309-314. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-23/