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.
E. H. has been supported by FONDECYT project n. 11170655 (Chile). Both authors have been supported by ECOS-Sud project n. C20E03 (France-Chile) and acknowledge financial support from the Inria Associated team ANACONDA.
The authors thank the anonymous referee for its valuable remarks that helped to improve its quality.
"Quasi-stationary distribution and metastability for the stochastic Becker-Döring model." Electron. Commun. Probab. 26 1 - 14, 2021. https://doi.org/10.1214/21-ECP411