Eyring-Kramers law for Fokker-Planck type differential operators

Jean-François Bony (1) , Dorian Le Peutrec (2) , Laurent Michel (1)

1 IMB - Institut de Mathématiques de Bordeaux
2 IDP - Institut Denis Poisson

We consider Fokker-Planck type differential operators associated with general Langevin processes admitting a Gibbs stationary distribution. Under assumptions insuring 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 which avoids supersymmetry or PT-symmetry assumptions.

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]; Probabilités [math.PR]

Jean-François Bony, Dorian Le Peutrec, Laurent Michel. Eyring-Kramers law for Fokker-Planck type differential operators. 2022. ⟨hal-03513124⟩