Quasi-stationary distribution and metastability for the stochastic Becker-Döring model

Erwan Hingant (1) , Romain Yvinec (2, 3)

1 UBB - Universidad del Bio Bio [Concepción]
2 PRC - Physiologie de la reproduction et des comportements [Nouzilly]
3 MUSCA - Dynamiques de populations multi-échelles pour des systèmes physiologiques

We study a stochastic version of the classical Becker-Döring model, a well-known kinetic model for cluster formation that predicts the existence of a long-lived metastable state before a thermodynamically unfavorable nucleation occurs, leading to a phase transition phenomena. This continuous-time Markov chain model has received little attention, compared to its deterministic differential equations counterpart. We show that the stochastic formulation leads to a precise and quantitative description of stochastic nucleation events thanks to an exponentially ergodic quasi-stationary distribution for the process conditionally on nucleation has not yet occurred.

Mots clés: Metastability; Exponential ergodicity; Becker-D&#246ring; Phase transition; Nucleation; Quasi-stationary distribution

Domaines: Probabilités [math.PR]

Erwan Hingant, Romain Yvinec. Quasi-stationary distribution and metastability for the stochastic Becker-Döring model. Electronic Communications in Probability, 2021, 26, ⟨10.1214/21-ECP411⟩. ⟨hal-03110670⟩