Free Infinite Divisibility of Free Multiplicative Mixtures of the Wigner Distribution View Full Text


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Article Info

DATE

2012-03

AUTHORS

Victor Pérez-Abreu, Noriyoshi Sakuma

ABSTRACT

Let I* and I⊞ be the classes of all classical infinitely divisible distributions and free infinitely divisible distributions, respectively, and let Λ be the Bercovici–Pata bijection between I* and I⊞. The class type W of symmetric distributions in I⊞ that can be represented as free multiplicative convolutions of the Wigner distribution is studied. A characterization of this class under the condition that the mixing distribution is 2-divisible with respect to free multiplicative convolution is given. A correspondence between symmetric distributions in I⊞ and the free counterpart under Λ of the positive distributions in I* is established. It is shown that the class type W does not include all symmetric distributions in I⊞ and that it does not coincide with the image under Λ of the mixtures of the Gaussian distribution in I*. Similar results for free multiplicative convolutions with the symmetric arcsine measure are obtained. Several well-known and new concrete examples are presented. More... »

PAGES

100-121

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10959-010-0288-5

DOI

http://dx.doi.org/10.1007/s10959-010-0288-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1019338589


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