Long time behavior of the solutions to non-linear Kraichnan equations
| dc.creator | Guionnet, Alice | |
| dc.creator | Mazza, Christian | |
| dc.date | 2004-09-16 | |
| dc.date.accessioned | 2026-07-07T05:12:11Z | |
| dc.date.available | 2026-07-07T05:12:11Z | |
| dc.description | We consider the solution of a nonlinear Kraichnan equation $$\partial_s H(s,t)=\int_t^s H(s,u)H(u,t) k(s,u) du,\quad s\ge t$$ 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. | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409274 | |
| dc.identifier | http://arxiv.org/abs/math/0409274 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72492 | |
| dc.subject | Probability | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Operator Algebras | |
| dc.subject | 82B44, 46L54, 45G10 | |
| dc.title | Long time behavior of the solutions to non-linear Kraichnan equations | |
| dc.type | text |