Geodesic
Fuss-Catalan numbers in noncommutative probability
Documenta mathematica, Tome 15 (2010), pp. 939-955
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We prove that if p,r∈R,p≥1 and 0lerlep then the Fuss-Catalan sequence (mmp+r​)mp+rr​ is positive definite. We study the family of the corresponding probability measures μ(p,r) on R from the point of view of noncommutative probability. For example, we prove that if 0le2rlep and r+1lep then μ(p,r) is ⊞-infinitely divisible. As a by-product, we show that the sequence m!mm​ is positive definite and the corresponding probability measure is ⊠-infinitely divisible.
DOI : 10.4171/dm/318
Classification : 44A60, 46L54, 60C05
Mots-clés : fuss-Catalan numbers, free, Boolean and monotonic convolution 
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     author = {Wojciech Mlotkowski},
     title = {Fuss-Catalan numbers in noncommutative probability},
     journal = {Documenta mathematica},
     pages = {939--955},
     year = {2010},
     volume = {15},
     doi = {10.4171/dm/318},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/318/}
}
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Wojciech Mlotkowski. Fuss-Catalan numbers in noncommutative probability. Documenta mathematica, Tome 15 (2010), pp. 939-955. doi: 10.4171/dm/318

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