On the Hausdorff continuity of free Lèvy processes and free convolution semigroups

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2018Embargo end date: 01 Oct 2015 English Publisher:Elsevier BVJournal:Journal of Mathematical Analysis and Applications, volume 459, pages 604-613 (issn: 0022-247X,

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Authors: Williams, John D.;

doi: 10.1016/j.jmaa.2016.09.062 , 10.48550/arxiv.1510.00003

arXiv: 1510.00003

On the Hausdorff continuity of free Lèvy processes and free convolution semigroups

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Abstract

Let $μ$ denote a Borel probability measure and let $\{ μ_{t} \}_{t\geq 1}$ denote the free additive convolution semigroup of Nica and Speicher. We show that the support of these measures varies continuously in the Hausdorff metric for $t >1$. We utilize complex analytic methods and, in particular, a characterization of the absolutely continuous portion of these supports due to Huang.

Small revisions at the referees behest. To be published in the Journal of Mathematical Analysis and its Applications

Related Organizations

Saarland University
Germany

Keywords

Probability (math.PR), Mathematics - Operator Algebras, Processes with independent increments; Lévy processes, free probability, semigroups, Free probability and free operator algebras, Mathematics - Classical Analysis and ODEs, Nevanlinna functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Operator Algebras (math.OA), 46L54, 30E20, Mathematics - Probability

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