The Eyring-Kramers law for Markovian jump processes with symmetries

Nils Berglund and Sébastien Dutercq
J. Theoretical Probability, 29 (4):1240-1279 (2016)

We prove an Eyring-Kramers law for the small eigenvalues and mean first-passage times of a metastable Markovian jump process which is invariant under a group of symmetries. Our results show that the usual Eyring-Kramers law for asymmetric processes has to be corrected by a factor computable in terms of stabilisers of group orbits. Furthermore, the symmetry can produce additional Arrhenius exponents and modify the spectral gap. The results are based on representation theory of finite groups.

Mathematical Subject Classification: 60J27 (primary), 20C35, 60K35 (secondary).

Keywords and phrases: Metastability, Kramers' law, stochastic exit problem, first-passage time, Markovian jump process, spectral theory, symmetry group, representation theory.

 

Journal Homepage Published article: 10.1007/s10959-015-0617-9 MR3571245 Zbl1365.60074

PDF file (468 Kb) hal-00913302 arXiv/1312.0835