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On Asymptotic Growth of the Support of Free Multiplicative Convolutions


 
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1. Title Title of document On Asymptotic Growth of the Support of Free Multiplicative Convolutions
 
2. Creator Author's name, affiliation, country Vladislav Kargin; Courant Institute of Mathematical Sciences
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Free probability, free multiplicative convolution
 
3. Subject Subject classification 46L54, 15A52
 
4. Description Abstract Let $\mu$ be a compactly supported probability measure on $\mathbb{R}^{+}$ with expectation $1$ and variance $V.$ Let $\mu _{n}$ denote the $n$-time free multiplicative convolution of measure $\mu $ with itself. Then, for large $n$ the length of the support of $\mu _{n}$ is asymptotically equivalent to $eVn$, where $e$ is the base of natural logarithms, $ e=2.71\ldots $.
 
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7. Date (YYYY-MM-DD) 2008-07-09
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1396
 
10. Identifier Digital Object Identifier 10.1214/ECP.v13-1396
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 13
 
12. Language English=en
 
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