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On a remarkable semigroup of homomorphisms with respect to free multiplicative convolution
, 2008
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Multivariable subordination distributions for free additive convolution
, 2008
"... Let k be a positive integer and let Dc k denote the space of joint distributions for ktuples of selfadjoint elements in Cprobability space. The paper studies the concept of “subordination distribution of µ�ν with respect to ν ” for µ, ν Dc k, where� is the operation of free additive convolution on ..."
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Let k be a positive integer and let Dc k denote the space of joint distributions for ktuples of selfadjoint elements in Cprobability space. The paper studies the concept of “subordination distribution of µ�ν with respect to ν ” for µ, ν Dc k, where� is the operation of free additive convolution on Dc k. The main tools used in this study are combinatorial properties of Rtransforms for joint distributions and a related operator model, with operators acting on the full Fock space. Multivariable subordination turns out to have nice relations to a process of evolution towards�infinite divisibility on Dc k that was recently found by Belinschi and Nica (arXiv:0711.3787). Most notably, one gets better insight into a connection which this process was known to have with free Brownian motion.
Noncrossing linked partitions, the partial order�on NC n, and the Stransform
, 901
"... The paper establishes a connection between two recent combinatorial developments in free probability: the noncrossing linked partitions introduced by Dykema in 2007 to study the Stransform, and the partial order�on NC n introduced by Belinschi and Nica in 2008 in order to study relations between f ..."
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The paper establishes a connection between two recent combinatorial developments in free probability: the noncrossing linked partitions introduced by Dykema in 2007 to study the Stransform, and the partial order�on NC n introduced by Belinschi and Nica in 2008 in order to study relations between free and Boolean probability. More precisely, one has a canonical bijection between NCL n (the set of all noncrossing linked partitions of 1,...,n) and the set α, β�α, β NC n, α�β. As a consequence of this bijection, one gets an alternative description of Dykema’s formula expressing the moments of a noncommutative random variable a in terms of the coefficients of the reciprocal Stransform 1 Sa. Moreover, due to the Boolean features of�, this formula can be simplified to a form which resembles the momentcumulant formula from cfree probability. 1.
Noncrossing linkedpartitions, the partial order�on NC n, and the Stransform
, 901
"... The paper establishes a connection between two recent combinatorial developments in free probability: the noncrossing linkedpartitions introduced by Dykema in 2007 to study the Stransform, and the partial order�on NC n introduced by Belinschi and Nica in 2008 in order to study relations between f ..."
Abstract
 Add to MetaCart
The paper establishes a connection between two recent combinatorial developments in free probability: the noncrossing linkedpartitions introduced by Dykema in 2007 to study the Stransform, and the partial order�on NC n introduced by Belinschi and Nica in 2008 in order to study relations between free and Boolean probability. More precisely, one has a canonical bijection between NCL n (the set of all noncrossing linkedpartitions of 1,...,n) and the set α, β�α, β NC n, α�β. As a consequence of this bijection, one gets an alternative description of Dykema’s formula expressing the moments of a noncommutative random variable a in terms of the coefficients of the reciprocal Stransform 1 Sa. Moreover, due to the Boolean features of�, this formula can be simplified to a form which resembles the momentcumulant formula from cfree probability. 1.