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2008 On Asymptotic Growth of the Support of Free Multiplicative Convolutions
Vladislav Kargin
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Electron. Commun. Probab. 13: 415-421 (2008). DOI: 10.1214/ECP.v13-1396


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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Vladislav Kargin. "On Asymptotic Growth of the Support of Free Multiplicative Convolutions." Electron. Commun. Probab. 13 415 - 421, 2008.


Accepted: 9 July 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1193.46041
MathSciNet: MR2424965
Digital Object Identifier: 10.1214/ECP.v13-1396

Primary: 46L54
Secondary: 15A52

Keywords: free multiplicative convolution , Free probability

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