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A free stochastic partial differential equation

Yoann Dabrowski (2014)

Annales de l'I.H.P. Probabilités et statistiques

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 R ω embeddable. This includes an N -tuple of q -Gaussian random variables e.g. for | q | N 0 . 13 .

A log-Sobolev type inequality for free entropy of two projections

Fumio Hiai, Yoshimichi Ueda (2009)

Annales de l'I.H.P. Probabilités et statistiques

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 noncommutative version of a Theorem of Marczewski for submeasures

Paolo de Lucia, Pedro Morales (1992)

Studia Mathematica

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 recursion formula for the moments of the gaussian orthogonal ensemble

M. Ledoux (2009)

Annales de l'I.H.P. Probabilités et statistiques

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

Rafał Sałapata (2011)

Banach Center Publications

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]).

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