Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond

Details Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond

2012-02-05

arxiv.org/abs/1202.0990v1

Mathematics

Probability

62 pages, 4 figures

Scientific paper

We prove a Kramers-type law for metastable transition times for a class of one-dimensional parabolic stochastic partial differential equations (SPDEs) with bistable potential. The expected transition time between local minima of the potential energy depends exponentially on the energy barrier to overcome, with an explicit prefactor related to functional determinants. Our results cover situations where the functional determinants vanish owing to a bifurcation, thereby rigorously proving the results of formal computations announced in [Berglund and Gentz, J. Phys. A 42:052001 (2009)]. The proofs rely on a spectral Galerkin approximation of the SPDE by a finite-dimensional system, and on a potential-theoretic approach to the computation of transition times in finite dimension.

Affiliated with

Also associated with

No associations

Rating

Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-461901