46 citations · 128 across the 37 of their papers we have counts for
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Free Infinite Divisibility for Ultrasphericals
Octavio Arizmendi, Serban T. Belinschi
We prove that the integral powers of the semicircular distribution are freely infinitely divisible. As a byproduct we get another proof of the free infnite divisibility of the clas…
Classical and free infinite divisibility for Boolean stable laws
Octavio Arizmendi, Takahiro Hasebe
We completely determine the free infinite divisibility for the Boolean stable law which is parametrized by a stability index and an asymmetry coefficient . We prove that the…
k-Divisible random variables in free probability
Octavio Arizmendi
We introduce and study the notion of k-divisible elements in a non-commutative probability space. A k-divisible element is a (non-commutative) random variable whose n-th moment van…
Products of free random variables and k-divisible partitions
Octavio Arizmendi, Carlos Vargas
We derive a formula for the moments and the free cumulants of the multiplication of free random variables in terms of -equal and -divisible non-crossing partitions. This…
Statistics of blocks in k-divisible non-crossing partitions
Octavio Arizmendi
We derive a formula for the expected number of blocks of a given size from a non-crossing partition chosen uniformly at random. Moreover, we refine this result subject to the restr…
On the Law of Free Subordinators
Octavio Arizmendi, Takahiro Hasebe, Noriyoshi Sakuma
We study the freely infinitely divisible distributions that appear as the laws of free subordinators. This is the free analog of classically infinitely divisible distributions supp…