%0 Unpublished work %T Diffusion in the space of complex Hermitian matrices - microscopic properties of the averaged characteristic polynomial and the averaged inverse characteristic polynomial %+ Service de Physique Théorique (SPhT) %A Blaizot, Jean-Paul %A Grela, Jacek %A Nowak, Maciej A. %A Warchoł, Piotr %Z 26 pages, 4 figures %8 2015-09-14 %D 2015 %Z 1405.5244 %Z Physics [physics]/Mathematical Physics [math-ph]Preprints, Working Papers, ... %X 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. %G English %L cea-01198674 %U https://cea.hal.science/cea-01198674 %~ CEA %~ CNRS %~ DSM-IPHT %~ TDS-MACS %~ CEA-DRF