Quasi-stationary distribution and metastability for the stochastic Becker-D\"oring model

TL;DR

This paper analyzes a stochastic version of the Becker-D"oring model, revealing how metastable states and nucleation events can be quantitatively described using a quasi-stationary distribution, providing insights into phase transition phenomena.

Contribution

It introduces a stochastic formulation of the Becker-D"oring model and characterizes its metastability and nucleation via a quasi-stationary distribution, advancing understanding of stochastic phase transitions.

Findings

Existence of an exponentially ergodic quasi-stationary distribution

Quantitative description of stochastic nucleation events

Metastability characterized by long-lived states before phase transition

Abstract

We study a stochastic version of the classical Becker-D\"oring 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.