Diffusion in the space of complex hermitian matrices : microscopic properties of the averaged characteristic polynomial and the averaged inverse characteristic polynomial

Bibliographic description

punktacja MNiSW [2015 A]: 15

title:	Diffusion in the space of complex hermitian matrices : microscopic properties of the averaged characteristic polynomial and the averaged inverse characteristic polynomial
author:	Blaizot Jean-Paul, Grela Jacek , Nowak Maciej , Warchoł Piotr
journal title:	Acta Physica Polonica. B
title of volume:	Random Matrix Theory : foundations and applications
volume:	46
issue:	9
date of publication :	2015
pages:	1801-1823
ISSN:	0587-4254
eISSN:	1509-5770
DOI:	10.5506/APhysPolB.46.1801
language:	English
journal language:	English
abstract in English:	We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with the 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 and for any initial condition assigned to the process. The solutions have compact integral representation that allows for a simple study of their asymptotic behavior, uncovering the Airy and Pearcey functions.
number of pulisher's sheets:	1,5
affiliation:	Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego
type:	journal article
subtype:	academic paper