English

On the Hausdorff Continuity of Free L\`evy Processes and Free Convolution Semigroups

Operator Algebras 2016-08-01 v2 Classical Analysis and ODEs Probability

Abstract

Let μ\mu denote a Borel probability measure and let {μt}t1\{ \mu_{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>1t >1. We utilize complex analytic methods and, in particular, a characterization of the absolutely continuous portion of these supports due to Huang.

Keywords

Cite

@article{arxiv.1510.00003,
  title  = {On the Hausdorff Continuity of Free L\`evy Processes and Free Convolution Semigroups},
  author = {John D. Williams},
  journal= {arXiv preprint arXiv:1510.00003},
  year   = {2016}
}

Comments

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