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 denote a Borel probability measure and let 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 . 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