7 February 2011
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.
- Partial Differential Equations Seminar