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Continuity and growth of free multiplicative convolution semigroups. (English) Zbl 1419.46041
Summary: Let $$\mu$$ be a compactly supported probability measure on the positive half-line and let $$\mu ^{\boxtimes t}$$ be the free multiplicative convolution semigroup. We show that the support of $$\mu ^{\boxtimes t}$$ varies continuously as $$t$$ changes. We also obtain the asymptotic length of the support of these measures.
##### MSC:
 46L54 Free probability and free operator algebras
Full Text:
##### References:
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