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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 40 open journal systems 


On Asymptotic Growth of the Support of Free Multiplicative Convolutions

Vladislav Kargin, Courant Institute of Mathematical Sciences


Abstract
Let μ be a compactly supported probability measure on the positive half-line with expectation 1 and variance V. Let μn denote the n-time free multiplicative convolution of μ with itself. Then, for large n the length of the support of μn is asymptotically equivalent to eVn, where e is the base of natural logarithms, e=2.71...


Full text: PDF

Pages: 415-421

Published on: July 9, 2008
Bibliography
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Electronic Communications in Probability. ISSN: 1083-589X