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

On Asymptotic Growth of the Support of Free Multiplicative Convolutions