On Asymptotic Growth of the Support of Free Multiplicative Convolutions
Vladislav Kargin, Courant Institute of Mathematical Sciences
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...