Eyring–Kramers law for Fokker–Planck type differential operators

  • Jean-François Bony

    Université de Bordeaux, Talence, France
  • Dorian Le Peutrec

    Université de Nantes, Nantes, France
  • Laurent Michel

    Université de Bordeaux, Talence, France
Eyring–Kramers law for Fokker–Planck type differential operators cover

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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.

Cite this article

Jean-François Bony, Dorian Le Peutrec, Laurent Michel, Eyring–Kramers law for Fokker–Planck type differential operators. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1461