89 citations · 202 across the 20 of their papers we have counts for
5 papers · 1 filter
Concavification of free entropy
Philippe Biane, Yoann Dabrowski
We introduce a modification of Voiculescu's free entropy which coincides with the liminf variant of Voiculescu's free entropy on extremal states, but is a concave upper semi-contin…
Free probability and combinatorics
Philippe Biane
A combinatorial approach to free probability theory has been developped by Roland Speicher, based on the notion of noncrossing cumulants, a free analogue of the classical theory of…
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…
Computation of some examples of Brown's spectral measure in free probability
Philippe Biane, Franz Lehner
We use free probability techniques for computing spectra and Brown measures of some non hermitian operators in finite von Neumann algebras. Examples include u_n+u_oo where u_n and…
Stable laws and domains of attraction in free probability theory
Hari Bercovici, Vittorino Pata, Philippe Biane
In this paper we determine the distributional behavior of sums of free (in the sense of Voiculescu) identically distributed, infinitesimal random variables. The theory is shown to…