The Extent of Correlations in a Stochastic Coalescence Process

Abstract

A stochastic model of coalescence is set up and solved for the probabilities of all possible histories of particle growth. The full stochastic model is compared with the so-called kinetic model to which it reduces in the absence of correlations. A primary objective is the assessment of the extent of correlations in poorly mixed systems or in systems of small populations. The study shows that insofar as the total number of particles is concerned, regardless of their size distribution, the results from the kinetic equations match the true stochastic averages even for very small initial populations. But, when size distributors are considered, then, in systems of small population or in large systems that are poorly mixed, the results of the kinetic equations may differ substantially from the stochastic means in the long-term tail; apart from the tail, the distributions from the full stochastic and kinetic models match quite well.