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The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory

Saitoh N., Yoshida H.

Probability and Mathematical Statistics

2001

Vol. 21, Fasc. 1

159--170

We calculate Voiculescu’s R-transform of the compactly supported probability measure on Rinduced from the orthogonal polynomials with a constant recursion formula, and investigate its infinite divisibility with respect to the additive free convolution. In the case of infinite divisibility, we give the Lévy-Hinčin measure explicitly for the integral representation of the R-transform of the free analogue of the Lévy-Hinčin formula.