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On Asymptotic Growth of the Support of Free Multiplicative Convolutions

   
@article{ECP1396,
	author = {Vladislav Kargin},
	title = {On Asymptotic Growth of the Support of Free Multiplicative Convolutions},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {Free probability, free multiplicative convolution},
	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 $.},
	pages = {no. 40, 415-421},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1396},    
        url = {http://ecp.ejpecp.org/article/view/1396}}