Continuity and growth of free multiplicative convolution semigroups

2017/09/20 by Xiaoxue Deng, Deng, Xiaoxue, Ping Zhong +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1709.07060

openalex publication_date 2017/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let μ be a compactly supported probability measure on the positive half-line and let μ^{\boxtimes t} be the free multiplicative convolution semigroup. We show that the support of μ^{\boxtimes t} varies continuously as t changes. We also obtain the asymptotic length of the support of these measures.

Citations

• On the Free Convolution with a Free Multiplicative Analogue of the Normal Distribution

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