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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.
46L54 Free probability and free operator algebras
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