AbstractWe prove that the classical normal distribution is infinitely divisible with respect to the free additive convolution. We study the Voiculescu transform first by giving a survey of its combinatorial implications and then analytically, including a proof of free infinite divisibility. In fact we prove that a sub-family of Askey–Wimp–Kerov distributions are freely infinitely divisible, of which the normal distribution is a special case. At the time of this writing this is only the third example known to us of a nontrivial distribution that is infinitely divisible with respect to both classical and free convolution, the others being the Cauchy distribution and the free 1/2-stable distribution
Infinitely divisible random variables have distributions that can be written as sums of countably ma...
The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Prec...
In this paper, a survey is given of some recent developments in infinite divisibility. There are thr...
There is a one-to-one correspondence between classical one-dimensional infi-nitely divisible distrib...
We study the freely infinitely divisible distributions that appear as the laws of free subordinators...
In a previous paper ([B-G1]), we defined the rectangular free convolution λ. Here, we investigate th...
Belinschi et al. [Adv. Math., 226 (2011), 3677--3698] proved that the normal distribution is freely ...
We prove that $X^r$ follows a free regular distribution, i.e. the law of a nonnegative free Lévy pro...
The class of $R$-diagonal $*$-distributions is fairly well understood in free probability. In this c...
In the present paper we define and investigate a novel class of distributions on the simplex, termed...
The principles of infinite divisibility are discussed, and illustrated by their occurrence in statis...
We study infinitely divisible (ID) distributions on the nonnegative half-line $\mathbb{R}_+$. The L\...
We construct a random matrix model for the bijection between clas-sical and free infinitely divisib...
In this paper we continue our studies, initiated in [BT1],[BT2] and [BT3], of the con-nections betwe...
none2The article provides an historical survey of the early contributions on infinitely divisible di...
Infinitely divisible random variables have distributions that can be written as sums of countably ma...
The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Prec...
In this paper, a survey is given of some recent developments in infinite divisibility. There are thr...
There is a one-to-one correspondence between classical one-dimensional infi-nitely divisible distrib...
We study the freely infinitely divisible distributions that appear as the laws of free subordinators...
In a previous paper ([B-G1]), we defined the rectangular free convolution λ. Here, we investigate th...
Belinschi et al. [Adv. Math., 226 (2011), 3677--3698] proved that the normal distribution is freely ...
We prove that $X^r$ follows a free regular distribution, i.e. the law of a nonnegative free Lévy pro...
The class of $R$-diagonal $*$-distributions is fairly well understood in free probability. In this c...
In the present paper we define and investigate a novel class of distributions on the simplex, termed...
The principles of infinite divisibility are discussed, and illustrated by their occurrence in statis...
We study infinitely divisible (ID) distributions on the nonnegative half-line $\mathbb{R}_+$. The L\...
We construct a random matrix model for the bijection between clas-sical and free infinitely divisib...
In this paper we continue our studies, initiated in [BT1],[BT2] and [BT3], of the con-nections betwe...
none2The article provides an historical survey of the early contributions on infinitely divisible di...
Infinitely divisible random variables have distributions that can be written as sums of countably ma...
The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Prec...
In this paper, a survey is given of some recent developments in infinite divisibility. There are thr...