A generalized Biane process
A linear Radon-Nikodym type theorem for -algebras with applications to measure theory
A mixed quantum-classical central limit theorem
A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex parameter is shown.
A new proof for the multiplicative property of the boolean cumulants with applications to the operator-valued case
The paper presents several combinatorial properties of the boolean cumulants. A consequence is a new proof of the multiplicative property of the boolean cumulant series that can be easily adapted to the case of boolean independence with amalgamation over an algebra.
A non-commutative central limit theorem.
A noncommutative version of a Theorem of Marczewski for submeasures
It is shown that every monocompact submeasure on an orthomodular poset is order continuous. From this generalization of the classical Marczewski Theorem, several results of commutative Measure Theory are derived and unified.
A projective central limit theorem and interacting Fock space representation for the limit process
Accardi et al. proved a central limit theorem, based on the notion of projective independence. In this note we use the symmetric projective independence to present a new version of that result, where the limiting process is perturbed by the insertion of suitable test functions. Moreover we give a representation of the limit process in 1-mode type interacting Fock space.
A remark on p-convolution
We introduce a p-product of algebraic probability spaces, which is the definition of independence that is natural for the model of noncommutative Brownian motions, described in [10] (for q = 1). Using methods of the conditionally free probability (cf. [4, 5]), we define a related p-convolution of probability measures on ℝ and study its relations with the notion of subordination (cf. [1, 8, 9, 13]).
Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries
The notion of monoidal equivalence for compact quantum groups was recently introduced by Bichon, De Rijdt and Vaes. In this paper we prove that there is a natural bijective correspondence between actions of monoidally equivalent quantum groups on unital -algebras or on von Neumann algebras. This correspondence turns out to be very useful to obtain the behavior of Poisson and Martin boundaries under monoidal equivalence of quantum groups. Finally, we apply these results to identify the Poisson boundary...
Algèbres de von Neumann de groupes libres et probabilités non commutatives
Almost sure convergence of iterates of contractions in noncommutative L2-spaces.
An Analogue of a Hardy-Littlewood-Fejér Inequality for Upper Triangular Trace Class Operators.
An individual ergodic theorem on the Hilbert space logic
Application du «bébé Fock» au modèle d'Ising
Applications du théorème de factorisation pour des fonctions à valeurs opérateurs
Approximating the Fock space with the toy Fock space
Arens algebras, associated with commutative von Neumann algebras
Asymptotic spectral analysis of generalized Erdős-Rényi random graphs
Motivated by the Watts-Strogatz model for a complex network, we introduce a generalization of the Erdős-Rényi random graph. We derive a combinatorial formula for the moment sequence of its spectral distribution in the sparse limit.
Asymptotic spectral analysis of growing graphs: odd graphs and spidernets
Two new examples are given for illustrating the method of quantum decomposition in the asymptotic spectral analysis for a growing family of graphs. The odd graphs form a growing family of distance-regular graphs and the two-sided Rayleigh distribution appears in the limit of vacuum spectral distribution of the adjacency matrix. For a spidernet as well as for a growing family of spidernets the vacuum distribution of the adjacency matrix is the free Meixner law. These distributions are calculated...
Asymptotic spectral distributions of distance k-graphs of large-dimensional hypercubes
We derive the asymptotic spectral distribution of the distance k-graph of N-dimensional hypercube as N → ∞.