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2021 Quasi-stationary distribution and metastability for the stochastic Becker-Döring model
Erwan Hingant, Romain Yvinec
Author Affiliations +
Electron. Commun. Probab. 26: 1-14 (2021). DOI: 10.1214/21-ECP411


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.

Funding Statement

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.


Download Citation

Erwan Hingant. Romain Yvinec. "Quasi-stationary distribution and metastability for the stochastic Becker-Döring model." Electron. Commun. Probab. 26 1 - 14, 2021.


Received: 15 August 2020; Accepted: 16 June 2021; Published: 2021
First available in Project Euclid: 7 July 2021

Digital Object Identifier: 10.1214/21-ECP411

Primary: 60J27, 82C26


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