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Free infinite divisibility for powers of random variables

open access: yesFree infinite divisibility for powers of random variables
We prove that $X^r$ follows a free regular distribution, i.e. the law of a nonnegative free Lévy process if: (1) $X$ follows a free Poisson distribution without an atom at 0 and $r ∈ (−∞, 0] ∪ [1,∞)$; (2) $X$ follows a free Poisson distribution with an atom at 0 and $r ≥ 1$; (3) $X$ follows a mixture of some HCM distributions and $|r| ≥ 1$; (4) $X ...
openaire  

Semicircle law, free random variables and entropy

open access: yes, 2014
Petz, Dňes, Hiai, Fumio
core  

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