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Limit theorems for free Levy processes

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Title: Limit theorems for free Levy processes
Authors: Arizmendi, Octavio Browse this author
Hasebe, Takahiro Browse this author →KAKEN DB
Keywords: free Levy processes
multiplicative convolutions
Boolean independence
limit theorems
small times
Issue Date: 17-Apr-2019
Publisher: University of Washington
Journal Title: Electronic journal of probability
Volume: 23
Start Page: 101
Publisher DOI: 10.1214/18-EJP224
Abstract: We consider different limit theorems for additive and multiplicative free Levy processes. The main results are concerned with positive and unitary multiplicative free Levy processes at small times, showing convergence to log free stable laws for many examples. The additive case is much easier, and we establish the convergence at small or large times to free stable laws. During the investigation we found out that a log free stable law with index 1 coincides with the Dykema-Haagerup distribution. We also consider limit theorems for positive multiplicative Boolean Levy processes at small times, obtaining log Boolean stable laws in the limit.
Type: article
URI: http://hdl.handle.net/2115/73687
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 長谷部 高広

 

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