A free analogue of the transportation cost inequality on the circle
A free stochastic partial differential equation
We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming also the von Neumann algebra embeddable. This includes an -tuple of -Gaussian random variables e.g. for .
A generalized Biane process
A linear Radon-Nikodym type theorem for -algebras with applications to measure theory
A log-Sobolev type inequality for free entropy of two projections
We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of two projections.
A matrix representation of the Bercovici-Pata bijection.
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 note on regularity for free convolutions
A note on the von Neumann algebra underlying some universal compact quantum groups.
A proof of a non-commutative central limit theorem by the Lindeberg method.
A recursion formula for the moments of the gaussian orthogonal ensemble
We present an analogue of the Harer–Zagier recursion formula for the moments of the gaussian Orthogonal Ensemble in the form of a five term recurrence equation. The proof is based on simple gaussian integration by parts and differential equations on Laplace transforms. A similar recursion formula holds for the gaussian Symplectic Ensemble. As in the complex case, the result is interpreted as a recursion formula for the number of 1-vertex maps in locally orientable surfaces with a given number of...
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]).
A survey on dilations of projective isometric representations.
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