Low lying eigenvalues and convergence to the equilibrium of some Piecewise Deterministic Markov Processes generators in the small temperature regime

Arnaud Guillin (1, 2) , Boris Nectoux (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

In this work we study the number of small eigenvalues and the convergence to the equilibrium of the Bouncy Particle Sampler process and the Zig-Zag process generators in the small temperature regime. Such processes, which fall in the class of Piecewise Deterministic Markov Processes, are non diffusive and non reversible.

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

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Probabilités [math.PR]; Théorie spectrale [math.SP]

Arnaud Guillin, Boris Nectoux. Low lying eigenvalues and convergence to the equilibrium of some Piecewise Deterministic Markov Processes generators in the small temperature regime. Annales Henri Poincaré, 2020, 21 (11), pp.3575-3608. ⟨10.1007/s00023-020-00949-7⟩. ⟨hal-02436593v3⟩