On time dynamics of coagulation-fragmentation processes

TL;DR

This paper characterizes coagulation-fragmentation processes with time-homogeneous group count dynamics, extending mean-field Gibbs models, broadening solvable models, and answering a question posed by Berestycki and Pitman.

Contribution

It provides a new characterization of coagulation-fragmentation processes with time-homogeneous total group counts and extends the class of solvable mean-field Gibbs models.

Findings

Characterization of processes with time-homogeneous group count dynamics

Extension of mean-field Gibbs coagulation-fragmentation models

Answer to a question by Berestycki and Pitman

Abstract

We establish a characterization of coagulation-fragmentation processes, such that the induced birth and death processes depicting the total number of groups at time $t\ge 0$ are time homogeneous. Based on this, we provide a characterization of mean-field Gibbs coagulation-fragmentation models, which extends the one derived by Hendriks et al. As a by- product of our results, the class of solvable models is widened and a question posed by N. Berestycki and Pitman is answered, under restriction to mean-field models.