Long time behaviour of the solution to non-linear Kraichnan equations

• 成果类型: Article
• 署名作者: Guionnet, A; Mazza, C
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Geneva
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0382-7
• 发表日期: 2005
• 页码: 493-518
• 关键词: dynamics; MODEL

摘要

We consider the solution of a nonlinear Kraichnan equation partial derivative H-s(s, t) = integral(s)(t) H(s, u) H(u, t) k(s, u) du, s >= t with a covariance kernel k and boundary condition H( t, t) = 1. We study the long time behaviour of H as the time parameters t, s go to infinity, according to the asymptotic behaviour of k. This question appears in various subjects since it is related with the analysis of the asymptotic behaviour of the trace of non-commutative processes satisfying a linear differential equation, but also naturally shows up in the study of the so-called response function and aging properties of the dynamics of some disordered spin systems.