15 citations · 21 across the 3 of their papers we have counts for
6 papers · 1 filter
Free extreme values
Gerard Ben Arous, Dan Virgil Voiculescu
Free probability analogs of the basics of extreme-value theory are obtained, based on Ando's spectral order. This includes classification of freely max-stable laws and their domain…
Free Analysis Questions I: Duality Transform for the Coalgebra of
Dan Voiculescu
A duality transform for the coalgebra of the free difference quotient derivation-multiplication of an operator with respect to a free algebra of scalars is constructed. The dual ob…
The topological version of free entropy
Dan Voiculescu
Notions of topological free entropy and of free capacity are introduced in the -algebra context. Basic properties, basic problems and connections to potential theory and rando…
Analytic Subordination Consequences of Free Markovianity
Dan Voiculescu
Using simple operator-valued analytic function considerations several general analytic subordination results for a freely Markovian triple of operator algebras are derived from the…
Free Entropy
Dan Voiculescu
Free entropy is the analogue of entropy in free probability theory. The paper is a survey of free entropy, its applications to von Neumann algebras, connections to random matrix th…
A Free Probability Analogue of the Wasserstein Metric on the Trace-State Space
Philippe Biane, Dan Voiculescu
We define a free probability analogue of the Wasserstein metric, which extends the classical one. In dimension one, we prove that the square of the Wasserstein distance to the semi…