TY  - JOUR
A1  - Bovier, Anton
A1  - Eckhoff, Michael
A1  - Gayrard, Veronique
A1  - Klein, Markus
T1  - Metastability in reversible diffusion processes : I. Sharp asymptotics for capacities and exit times
N2  - We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form -epsilonDelta+ delF(.) del on R-d or subsets of R-d, where F is a smooth function with finitely many local minima. In analogy to previous work on 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 epsilon down arrow 0, to the capacities of suitably constructed sets. We show that these 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
Y1  - 2004
SN  - 1435-9855
ER  - 
TY  - JOUR
A1  - Bovier, Anton
A1  - Eckhoff, Michael
A1  - Gayrard, Veronique
A1  - Klein, Markus
T1  - Metastability and low-Lying spectra in reversible Markov chains
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Bovier, Anton
A1  - Eckhoff, Michael
A1  - Gayrard, Veronique
A1  - Klein, Markus
T1  - Metastability in stochastic dynamics of disordered mean-field models
Y1  - 2001
SN  - 0178-8051
ER  - 
TY  - THES
A1  - Eckhoff, Michael
T1  - Capacity and the low lying spectrum in attractive markov chains
Y1  - 2000
ER  - 
TY  - BOOK
A1  - Eckhoff, Michael
A1  - Klein, Markus
T1  - Long time behavior of one-dimensional stochastic dynamics
T3  - Preprint / SFB 288, Differentialgeometrie und Quantenphysik
Y1  - 2000
VL  - 455
PB  - TU Berlin, Mathematik Sonderforschungsbereich 288
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Klein, Markus
A1  - Bovier, Anton
A1  - Eckhoff, Michael
A1  - Gayrard, Véronique
T1  - Metastability and small eigenvalues in Markov chains
Y1  - 2000
ER  -