We review recent results on the metastable dynamics of systems of coupled stochastic differential equations in the weak-noise regime. While generic reversible systems can be described by the Eyring-Kramers law, which quantifies mean transition times and small eigenvalues of the generator, this law typically fails to describe the systems we are interested in. This is due both to the existence of a symmetry group, and to the existence of bifurcation points at which degenerate equilibria occur. We will describe extensions of the Eyring-Kramers law to such situations, as well as an extension to the limit of infinitely many coupled units, described by a parabolic stochastic PDE.
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References:
N.B and Sébastien Dutercq, The Eyring-Kramers law for Markovian jump processes with symmetries. To appear in J. Theoretical Probability (2015)
N.B and Barbara Gentz, The Eyring-Kramers law for potentials with nonquadratic saddles, Markov Processes Relat. Fields 16:549-598 (2010)
N.B and Barbara Gentz, Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond, Electronic J. Probability 18 (24):1-58 (2013)
| Subject : | : | oral |
| Topics | : | Statistical mechanics and computation of large deviation rate functions |
| PDF version | : |  PDF version |
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