On a ternary coalescent process

TL;DR

This paper introduces a novel ternary coalescent process, establishes its duality with a fragmentation process, and explores its asymptotic behavior, connecting it to the standard additive coalescent as the number of particles grows.

Contribution

It presents a new ternary coalescent model, provides a duality with fragmentation, and links the process to the standard additive coalescent through asymptotic analysis.

Findings

Duality between ternary coalescent and fragmentation processes.

Construction of the coalescent via random binary forests.

Convergence to the standard additive coalescent as N increases.

Abstract

We present a coalescent process where three particles merge at each coagulation step. Using a random walk representation, we prove duality with a fragmentation process, whose fragmentation law we specify explicitly. Furthermore, we give a second construction of the coalescence in terms of random binary forests and study asymptotic properties. Starting from N particles of unit mass, we obtain under an appropriate rescaling when N tends to infinity a well-known binary coalescence, the so-called standard additive coalescent.