A matrix interpolation between classical and free max operations: I. The   univariate case
  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 independent random variables. We present here a new insight on this analogy: its concrete realization based on random matrices giving an interpolation between classical and free settings. 
Florent Benaych-Georges (PMA, CMAP), Thierry Cabanal-Duvillard (MAP5)