Distributional symmetries and invariance principles in noncommutative probability theory provide sufficient conditions for the existence of central limit laws. In contrast to classical probability theory, there exist many different central limit laws for exchangeable sequences of noncommutative random variables and still little is known about their concrete form. This thesis goes one step further and investigates central limit laws for non-exchangeable spreadable sequences in the context of *-algebraic probability spaces. This provides first results on a new type of combinatorics underlying multivariate central limit theorems (CLTs). The starting point of the thesis has been a quite simple family of spreadable sequences, which is parametri...
. A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex p...
We consider second and third order limit theorems--namely central-limit theorems, Berry-Esseen bound...
In 1992, Speicher showed the fundamental fact that the probability measures playing the role of the ...
In the seventies, Charles Stein revolutionized the way of proving the Central Limit Theorem by intro...
AbstractA noncommutative generalization of the central limit theorem for even completely positive ma...
AbstractLet a multivariate sequence an(k) ⩾ 0 be given. Multivariate central and local limit theorem...
International audienceWe formulate and prove a general central limit theorem for sums of independent...
summary:MV-algebras can be treated as non-commutative generalizations of boolean algebras. The proba...
We prove a central limit theorem for non-commutative random variables in a von Neumann alge...
We discuss a central limit theorem in the framework of the group algebra of the Thompson group $F$. ...
AbstractFlajolet and Soria established several central limit theorems for the parameter ‘number of c...
AbstractLet {Xn}∞n=1be a sequence of free, identically distributed random variables with common dist...
Title changed. Major changes: results improved. 24 pagesInternational audienceIn this paper, we stud...
We show that the noncommutative Central Limit Theorem of Speicher can be adapted to produce the Gaus...
AbstractFlajolet and Soria (1989, 1990) discussed some general combinatorial structures in which cen...
. A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex p...
We consider second and third order limit theorems--namely central-limit theorems, Berry-Esseen bound...
In 1992, Speicher showed the fundamental fact that the probability measures playing the role of the ...
In the seventies, Charles Stein revolutionized the way of proving the Central Limit Theorem by intro...
AbstractA noncommutative generalization of the central limit theorem for even completely positive ma...
AbstractLet a multivariate sequence an(k) ⩾ 0 be given. Multivariate central and local limit theorem...
International audienceWe formulate and prove a general central limit theorem for sums of independent...
summary:MV-algebras can be treated as non-commutative generalizations of boolean algebras. The proba...
We prove a central limit theorem for non-commutative random variables in a von Neumann alge...
We discuss a central limit theorem in the framework of the group algebra of the Thompson group $F$. ...
AbstractFlajolet and Soria established several central limit theorems for the parameter ‘number of c...
AbstractLet {Xn}∞n=1be a sequence of free, identically distributed random variables with common dist...
Title changed. Major changes: results improved. 24 pagesInternational audienceIn this paper, we stud...
We show that the noncommutative Central Limit Theorem of Speicher can be adapted to produce the Gaus...
AbstractFlajolet and Soria (1989, 1990) discussed some general combinatorial structures in which cen...
. A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex p...
We consider second and third order limit theorems--namely central-limit theorems, Berry-Esseen bound...
In 1992, Speicher showed the fundamental fact that the probability measures playing the role of the ...