Eyring-Kramers type formulas for some piecewise deterministic Markov processes

Dorian Le Peutrec (1) , Laurent Michel (2) , Boris Nectoux (3)

1 IDP - Institut Denis Poisson
2 IMB - Institut de Mathématiques de Bordeaux
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

In this work, we give sharp asymptotic equivalents in the small temperature regime of the smallest eigenvalues of the generator of some piecewise deterministic Markov processes (including the ZigZag process and the Bouncy Particle Sampler process) with refreshment rate α on the one-dimensional torus T. These asymptotic equivalents are usually called Eyring-Kramers type formulas in the literature. The case when the refreshment rate α vanishes on T is also considered.

Mots clés: Piecewise Deterministic Markov Processes; small temperature regime; Eyring-Kramers formulas; metastability; spectral theory; semiclassical analysis

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]; Probabilités [math.PR]

Dorian Le Peutrec, Laurent Michel, Boris Nectoux. Eyring-Kramers type formulas for some piecewise deterministic Markov processes. 2023. ⟨hal-03553895v2⟩