Arens algebras, associated with commutative von Neumann algebras
Bibounded operators on W*-algebras.
bm-independence and central limit theorems associated with symmetric cones
We present a generalization of the classical central limit theorem to the case of non-commuting random variables which are bm-independent and indexed by a partially ordered set. As the set of indices I we consider discrete lattices in symmetric positive cones, with the order given by the cones. We show that the limit measures have moments which satisfy recurrences generalizing the recurrence for the Catalan numbers.
Calcul stochastique non commutatif
Central limit theorems for the brownian motion on large unitary groups
In this paper, we are concerned with the large limit of the distributions of linear combinations of the entries of a Brownian motion on the group of unitary matrices. We prove that the process of such a linear combination converges to a Gaussian one. Various scales of time and various initial distributions are considered, giving rise to various limit processes, related to the geometric construction of the unitary Brownian motion. As an application, we propose a very short proof of the asymptotic...
Centrally determined states on von Neumann algebras
It is shown that every von Neumann algebra whose centre determines the state space is already abelian.
Characterization of L...(M) for injective W*-algebras M.
Classification of injective factors: The work of Alain Connes.
Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces.
Computation of some examples of Brown's spectral measure in free probability
We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include where uₙ and are the generators of ℤₙ and ℤ respectively, in the free product ℤₙ*ℤ, or elliptic elements of the form where and are free semicircular elements of variance α and β.
Conditional Expectation and Bicontractive Projections on Jordan C*-algebras and Their Generalizations.
Construction de solutions d'«équations de structure»
Continuity and linear extensions of quantum measures on Jordan operator algebras.
Contracctive projections on operator triple systems.
Correction : «Éléments de probabilités quantiques. Calculs antisymétriques et «supersymétriques» en probabilités»
Corrections : «Éléments de probabilités quantiques (exposés I à V)»
Differential independence via an associative product of infinitely many linear functionals
We generalize the infinitesimal independence appearing in free probability of type B in two directions: to higher order derivatives and other natural independences: tensor, monotone and Boolean. Such generalized infinitesimal independences can be defined by using associative products of infinitely many linear functionals, and therefore the associated cumulants can be defined. These products can be seen as the usual natural products of linear maps with values in formal power series.
Éléments de probabilités quantiques (exposés VI à VIII)
Éléments de probabilités quantiques. X. Approximation de l'oscillateur harmonique (d'après L. Accardi et A. Bach)
Éléments de probabilités quantiques. XI. Caractérisation des lois de Bernoulli quantiques d'après K. R. Parthasarathy