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Explicit free multiplicative law of large numbers

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  • Raouf Fakhfakh

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.

Suggested Citation

  • Raouf Fakhfakh, 2023. "Explicit free multiplicative law of large numbers," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(7), pages 2031-2042, April.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:7:p:2031-2042
    DOI: 10.1080/03610926.2021.1944212
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