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)»