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 μ_{n} denote the n-time free multiplicative convolution of μ with itself.
Then, for large n the length of the support of μ_{n} is asymptotically equivalent to eVn,
where e is the base of natural logarithms, e=2.71...

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