Eyring–Kramers law for Fokker–Planck type differential operators

Abstract

We consider Fokker–Planck type differential operators associated with general Langevin processes admitting a Gibbs stationary distribution. Under assumptions ensuring suitable resolvent estimates, we prove Eyring–Kramers formulas for the bottom of the spectrum of these operators in the low temperature regime. Our approach is based on the construction of sharp Gaussian quasimodes and avoids supersymmetry or PT-symmetry assumptions.