%0 Unpublished work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