scholarly journals Continuity and growth of free multiplicative convolution semigroups

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Xiaoxue Deng ◽  
Ping Zhong
Keyword(s):  
Convolution Semigroups ◽  
Multiplicative Convolution ◽  
Free Multiplicative Convolution

scholarly journals New limit theorems related to free multiplicative convolution

2013 ◽  
Vol 214 (3) ◽  
pp. 251-264
Author(s):  
Noriyoshi Sakuma ◽  
Hiroaki Yoshida
Keyword(s):  
Limit Theorems ◽  
Multiplicative Convolution ◽  
Free Multiplicative Convolution

scholarly journals Regularity Properties of Free Multiplicative Convolution on the Positive Line

2020 ◽  
Author(s):  
Hong Chang Ji
Keyword(s):  
Probability Measures ◽  
Square Root ◽  
Continuous Part ◽  
Absolutely Continuous ◽  
Root Decay ◽  
Regularity Properties ◽  
Multiplicative Convolution ◽  
Free Multiplicative Convolution ◽  
Borel Probability ◽  
Positive Line

Abstract Given two nondegenerate Borel probability measures $\mu$ and $\nu$ on ${\mathbb{R}}_{+}=[0,\infty )$, we prove that their free multiplicative convolution $\mu \boxtimes \nu$ has zero singular continuous part and its absolutely continuous part has a density bounded by $x^{-1}$. When $\mu$ and $\nu$ are compactly supported Jacobi measures on $(0,\infty )$ having power law behavior with exponents in $(-1,1)$, we prove that $\mu \boxtimes \nu$ is another Jacobi measure whose density has square root decay at the edges of its support.

scholarly journals Hopf algebras and the logarithm of the S-transform in free probability ― Extended abstract

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Mitja Mastnak ◽  
Alexandru Nica
Keyword(s):  
Hopf Algebras ◽  
Free Probability ◽  
Algebraic Approach ◽  
S Transform ◽  
Multiplicative Convolution ◽  
Free Multiplicative Convolution ◽  
International Audience

International audience This document is an extended abstract of the paper `Hopf algebras and the logarithm of the S-transform in free probability' in which we introduce a Hopf algebraic approach to the study of the operation $\boxtimes$ (free multiplicative convolution) from free probability.

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