Fuss-Catalan numbers in noncommutative probability
Wojciech MlotkowskiMathematical Institute University of Wroclaw Pl. Grunwaldzki 2/4 50-384 Wroclaw Poland
We prove that if and then the Fuss-Catalan sequence is positive definite. We study the family of the corresponding probability measures on from the point of view of noncommutative probability. For example, we prove that if and then is -infinitely divisible. As a by-product, we show that the sequence is positive definite and the corresponding probability measure is -infinitely divisible.
Cite this article
Wojciech Mlotkowski, Fuss-Catalan numbers in noncommutative probability. Doc. Math. 15 (2010), pp. 939–955DOI 10.4171/DM/318