Abstract
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.
Citation
Xiaoxue Deng. Ping Zhong. "Continuity and growth of free multiplicative convolution semigroups." Electron. Commun. Probab. 24 1 - 11, 2019. https://doi.org/10.1214/18-ECP202
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