Seminar series
Date
Mon, 07 Feb 2011
17:00
17:00
Location
Gibson 1st Floor SR
Speaker
Grigoris Pavliotis
Organisation
Imperial College
In this talk we will present some recent results on the long time
asymptotics of the generalized (non-Markovian) Langevin equation (gLE). In particular,
we will discuss about the ergodic properties of the gLE and present estimates on the rate of convergence to equilibrium, we will present
a homogenization result (invariance principle) and we will discuss
about the convergence of the gLE dynamics to the (Markovian) Langevin
dynamics, in some appropriate asymptotic limit. The analysis is based on the approximation of the gLE by a
high (and possibly infinite) dimensional degenerate Markovian system,
and on the analysis of the spectrum of the generator of this Markov
process. This is joint work with M. Ottobre and K. Pravda-Starov.