Abstract: I will discuss a classical example featuring a metastable
behavior: finite-dimensional diffusion processes in the vanishing
noise limit. Exponential estimates have been introduced fifty years
ago by Freidlin and Wentzell. Recent developments in potential theory
and variational convergence allowed a refinement of those results. I
will focus on the non-reversible case, with motivations coming from
MCMC and open problems in the context of wKAM theory. The talk is
based on recent papers with G.DiGesu (TU Wien), C.Landim (IMPA) and
I.Seo (UC Berkeley/Seoul NU).
Abstract: I will talk about extending my earlier work on the vanishing noise limit of diffusions in noisy heteroclinic networks to longer time scales. In this field, the results are based on sequential analysis of exit locations and exit times for neighborhoods of unstable equilibria. The new results on exit times and the emergent hierarchical structure are joint with Zsolt Pajor-Gyulai.
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