Metastability in reversible diffusion processes invariant under a symmetry group

Sébastien Dutercq (1, 2)

1 FDP - Fédération de recherche Denis Poisson
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We extend the analysis of the problem of metastability of Markovian jump processes with symmetries, initiated in a previous work, to reversible diffusion processes. Using representation theory of finite groups, we prove an Eyring-Kramers law for the low-lying spectrum of the generator of the diffusion, thereby generalizing results by A. Bovier, V. Gayrard, and M. Klein.

Mots clés: Metastability; Kramers' law; stochastic exit problem; spectral gap; diffusion processes; spectral theory; potential theory; capacity; symmetry group; representation theory; first-passage time

Domaines: Mathématiques [math]

Sébastien Dutercq. Metastability in reversible diffusion processes invariant under a symmetry group. 2016. ⟨hal-01346069⟩