Explicit free multiplicative law of large numbers

Raouf Fakhfakh

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 7, 2031-2042

Abstract: Suppose Vν is the pseudo-variance function of the Cauchy–Stieltjes Kernel family K−(ν) generated by a non degenerate probability measure ν on the positive real line. We determine explicitly the law of large numbers μ for free multiplicative convolution given by Haagerup and Möller in terms of the pseudo-variance function Vν. Some examples of calculations of μ are given for probability measures ν of importance in free probability.

Date: 2023
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DOI: 10.1080/03610926.2021.1944212

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