We prove a central limit theorem for non-commutative random variables in a von Neumann algebra with a tracial state: Any non-commutative polynomial of averages of i.i.d. samples converges to a classical limit. The proof is based on a central limit theorem for ordered joint distributions together with a commutator estimate related to the Baker-Campbell-Hausdorff expansion. The result can be considered a generalization of Johansson's theorem on the limiting distribution of the shape of a random word in a fixed alphabet as its length goes to infinity [math.CO/9906120,math.PR/9909104]
We study the weak-convergence properties of random variables generated by unsharp quantum measuremen...
AbstractConsidering a random variable as a multiplication operator by a measurable function, a natur...
Distributional symmetries and invariance principles in noncommutative probability theory provide suf...
. A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex p...
We state and prove a noncommutative limit theorem for correlations which are homogeneous with respec...
International audienceWe formulate and prove a general central limit theorem for sums of independent...
In 1992, Speicher showed the fundamental fact that the probability measures playing the role of the ...
summary:MV-algebras can be treated as non-commutative generalizations of boolean algebras. The proba...
A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex par...
In this report we discuss some results of non--commutative (quantum) probability theory relating the...
Bringing forward the concept of convergence in moments from classical random variables to quantum ra...
We prove that all finite joint distributions of creation and annihilation operators in monotone and ...
A Central Limit Theorem is proved for linear random fields when sums are taken over union of finitel...
AbstractA noncommutative generalization of the central limit theorem for even completely positive ma...
We prove that all finite joint distributions of creation and annihilation operators in monotone and...
We study the weak-convergence properties of random variables generated by unsharp quantum measuremen...
AbstractConsidering a random variable as a multiplication operator by a measurable function, a natur...
Distributional symmetries and invariance principles in noncommutative probability theory provide suf...
. A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex p...
We state and prove a noncommutative limit theorem for correlations which are homogeneous with respec...
International audienceWe formulate and prove a general central limit theorem for sums of independent...
In 1992, Speicher showed the fundamental fact that the probability measures playing the role of the ...
summary:MV-algebras can be treated as non-commutative generalizations of boolean algebras. The proba...
A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex par...
In this report we discuss some results of non--commutative (quantum) probability theory relating the...
Bringing forward the concept of convergence in moments from classical random variables to quantum ra...
We prove that all finite joint distributions of creation and annihilation operators in monotone and ...
A Central Limit Theorem is proved for linear random fields when sums are taken over union of finitel...
AbstractA noncommutative generalization of the central limit theorem for even completely positive ma...
We prove that all finite joint distributions of creation and annihilation operators in monotone and...
We study the weak-convergence properties of random variables generated by unsharp quantum measuremen...
AbstractConsidering a random variable as a multiplication operator by a measurable function, a natur...
Distributional symmetries and invariance principles in noncommutative probability theory provide suf...