71 citations · 258 across the 47 of their papers we have counts for
5 papers · 2 filters
A continuous semigroup of notions of independence between the classical and the free one
Florent Benaych-Georges, Thierry Lévy
In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for non-commutative random variables. These noti…
On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions
Florent Benaych-Georges
n this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions t…
On a surprising relation between rectangular and square free convolutions
Florent Benaych-Georges
Debbah and Ryan have recently proved a result about the limit empirical singular distribution of the sum of two rectangular random matrices whose dimensions tend to infinity. In th…
A matrix interpolation between classical and free max operations: I. The univariate case
Florent Benaych-Georges, Thierry Cabanal-Duvillard
Recently, Ben Arous and Voiculescu considered taking the maximum of two free random variables and brought to light a deep analogy with the operation of taking the maximum of two in…
A permutation model for free random variables and its classical analogue
Florent Benaych-Georges, Ion Nechita
In this paper, we generalize a permutation model for free random variables which was first proposed by Biane in \cite{biane}. We also construct its classical probability analogue,…