On the Hausdorff Continuity of Free Lèvy Processes and Free Convolution Semigroups

2015/09/30 by Williams, John D.
#30E20 #46L54 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1510.00003

Abstract

Let μ denote a Borel probability measure and let \ μ_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.

Related

• Regularity results for free Lévy processes
• Supports of Measures in a free additive convolution semigroup
• Continuity and growth of free multiplicative convolution semigroups
• On the support of measures in multiplicative free convolution semigroups
• On a remarkable semigroup of homomorphisms with respect to free multiplicative convolution