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

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 $.

Citation

Download Citation

Vladislav Kargin. "On Asymptotic Growth of the Support of Free Multiplicative Convolutions." Electron. Commun. Probab. 13 415 - 421, 2008. https://doi.org/10.1214/ECP.v13-1396

Information

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

Subjects:
Primary: 46L54
Secondary: 15A52

JOURNAL ARTICLE
7 PAGES


SHARE
Back to Top