Diffusion in the space of complex Hermitian matrices - microscopic   properties of the averaged characteristic polynomial and the averaged inverse   characteristic polynomial
  We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial differential, diffusion-like, equations. These equations are valid for matrices of arbitrary size. Their solutions can be given an integral representation that allows for a simple study of their asymptotic behaviors for a broad range of initial conditions. 
Jean-Paul Blaizot, Jacek Grela, Maciej A. Nowak, Piotr Warcho{\l}
math-ph math.MP