The Lévy-Khintchine formula and Nica-Speicher property for deformations of the free convolution
Łukasz Jan Wojakowski (2007)
Banach Center Publications
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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...