• search hit 1 of 5
Back to Result List

Metastability in reversible diffusion processes I. Sharp asymptotics for capcities and exit times

Please always quote using this URN:urn:nbn:de:0296-matheon-969
  • We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form +rF ( )r on R or subsets of , where F is a smooth function with finitely many local minima. In analogy to previous work in discrete Markov chains, we show that metastable exit times from the attractive domains of the minima of F can be related, up to multiplicative errors that tend to one as # 0, to the capacities of suitably constructed sets. We show that this capacities can be computed, again up to multiplicative errors that tend to one, in terms of local characteristics of F at the starting minimum and the relevant saddle points. As a result, we are able to give the first rigorous proof of the classical Eyring-Kramers formula in dimension larger than 1. The estimates on capacities make use of their variational representation and monotonicity properties of Dirichlet forms. The methods developed here are extensions of our earlier work on discrete Markov chains to continuous diffusion processes.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Anton Bovier, Michael Eckhoff, Veronique Gayrard, Markus Klein
URN:urn:nbn:de:0296-matheon-969
Referee:Peter Imkeller
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2004/02/24
Release Date:2004/02/22
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
Preprint Number:93
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.