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arXiv · 1709.07060

Continuity and growth of free multiplicative convolution semigroups

Xiaoxue Deng·Ping Zhong
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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.

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Xiaoxue Deng, Ping Zhong. 2017-09-20. Continuity and growth of free multiplicative convolution semigroups. https://arxiv.org/abs/1709.07060

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