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Journal of Theoretical Probability

, Volume 29, Issue 4, pp 1240–1279 | Cite as

The Eyring–Kramers Law for Markovian Jump Processes with Symmetries

  • Nils BerglundEmail author
  • Sébastien Dutercq
Article

Abstract

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.

Keywords

Metastability Kramers’ law Stochastic exit problem First-passage time Markovian jump process Spectral theory Symmetry group Representation theory 

Mathematical Subject Classification

60J27 20C35 60K35 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Laboratoire MAPMO, CNRS UMR 7349, Fédération Denis Poisson, FR 2964Université d’OrléansOrléans Cedex 2France

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