| Contents |
| We consider systems of coupled overdamped ODEs perturbed by weak Gaussian white noise. Depending on coupling strength and noise intensities, their behaviour can range from Ising-model-like to globally synchronized dynamics. The long-time behaviour
of such systems is determined by the local minima and saddles of the associated potential energy landscape. In totally
asymmetric cases, the so-called metastable hierarchy determines expected transition times via the Eyring--Kramers formula.
However the systems we are interested in admit large symmetry groups, due to the symmetries of couplings and local interactions.
An approach based on representation theory for finite groups allows to determine a corrected formula for metastable transition
times in symmetric situations.
References:
Nils Berglund and S\'ebastien Dutercq,
The Eyring--Kramers law for Markovian jump processes with symmetries,
arXiv/1312.0835 (2013).
Nils Berglund and Barbara Gentz,
The Eyring--Kramers law for potentials with nonquadratic saddles,
Markov Processes Relat. Fields 16:549-598 (2010).
Nils Berglund, Bastien Fernandez and Barbara Gentz,
Metastability in interacting nonlinear stochastic differential equations I: From weak coupling to synchronisation,
Nonlinearity 20:2551-2581 (2007);
Metastability in interacting nonlinear stochastic differential equations II: Large-N behaviour,
Nonlinearity 20:2583-2614 (2007). |
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