Kramers' law: Validity, derivations and generalisations
N Berglund - arxiv preprint arxiv:1106.5799, 2011 - arxiv.org
Kramers' law describes the mean transition time of an overdamped Brownian particle
between local minima in a potential landscape. We review different approaches that have …
between local minima in a potential landscape. We review different approaches that have …
Generalisation of the Eyring–Kramers transition rate formula to irreversible diffusion processes
In the small noise regime, the average transition time between metastable states of a
reversible diffusion process is described at the logarithmic scale by Arrhenius' law. The …
reversible diffusion process is described at the logarithmic scale by Arrhenius' law. The …
Symmetries and zero modes in sample path large deviations
Sharp large deviation estimates for stochastic differential equations with small noise, based
on minimizing the Freidlin–Wentzell action functional under appropriate boundary …
on minimizing the Freidlin–Wentzell action functional under appropriate boundary …
Computing transition rates for the 1-D stochastic Ginzburg–Landau–Allen–Cahn equation for finite-amplitude noise with a rare event algorithm
In this article we compute and analyse the transition rates and duration of reactive
trajectories of the stochastic 1-D Allen–Cahn equations for both the Freidlin–Wentzell …
trajectories of the stochastic 1-D Allen–Cahn equations for both the Freidlin–Wentzell …
Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond
N Berglund, B Gentz - 2013 - projecteuclid.org
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 …
parabolic stochastic partial differential equations (SPDEs) with bistable potential. The …
Transitions amongst synchronous solutions in the stochastic Kuramoto model
L DeVille - Nonlinearity, 2012 - iopscience.iop.org
We consider the Kuramoto model of coupled oscillators with nearest-neighbour coupling
and additive white noise. We show that synchronous solutions which are stable without the …
and additive white noise. We show that synchronous solutions which are stable without the …
Cutoff thermalization for Ornstein–Uhlenbeck systems with small Lévy noise in the Wasserstein distance
This article establishes cutoff thermalization (also known as the cutoff phenomenon) for a
class of generalized Ornstein–Uhlenbeck systems (X t ε (x)) t⩾ 0 with ε-small additive Lévy …
class of generalized Ornstein–Uhlenbeck systems (X t ε (x)) t⩾ 0 with ε-small additive Lévy …
Using global invariant manifolds to understand metastability in the Burgers equation with small viscosity
The large-time behavior of solutions to the Burgers equation with small viscosity is described
using invariant manifolds. In particular, a geometric explanation is provided for a …
using invariant manifolds. In particular, a geometric explanation is provided for a …
Quantifying noisy attractors: from heteroclinic to excitable networks
Attractors of dynamical systems may be networks in phase space that can be heteroclinic
(where there are dynamical connections between simple invariant sets) or excitable (where …
(where there are dynamical connections between simple invariant sets) or excitable (where …
Metastability
A Bovier - Methods of contemporary mathematical statistical …, 1970 - Springer
Metastability is a wide-spread phenomenon in the dynamics of non-linear systems—
physical, chemical, biological or economic—subject to the action of temporal random forces …
physical, chemical, biological or economic—subject to the action of temporal random forces …