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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:459

Article

Williams, John D.¹ 

[1] Univ Saarland, Fachrichtung Math, Postfach 151150, D-66041 Saarbrucken, Germany

关键词: Free probability;    Semigroups;    Nevanlinna functions;   

DOI  :  10.1016/j.jmaa.2016.09.062

来源: Elsevier

【 摘 要 】

Let mu denote a Borel probability measure and let {mu(t)}(t >= 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. (C) 2016 Published by Elsevier Inc.

【 授权许可】

Free