Random walkers versus random crowds: diffusion of large matrices
  We briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative diffusion processes for hermitian and unitary ensembles. 
Ewa Gudowska-Nowak, Romuald J. Janik, Jerzy Jurkiewicz, Maciej A.   Nowak, Waldemar Wieczorek