Coupling any number of balls in the infinite-bin model

TL;DR

This paper demonstrates how to couple the behavior of any finite number of balls in the infinite-bin model with multiple transition rules, facilitating the analysis of convergence through regeneration events.

Contribution

It introduces a coupling method for finite balls in the infinite-bin model with multiple transition rules, enabling convergence analysis.

Findings

Coupling of finite balls under multiple transition rules established

Regeneration events are defined for convergence proofs

Enhances understanding of the infinite-bin model dynamics

Abstract

The infinite-bin model, introduced by Foss and Konstantopoulos, describes the Markovian evolution of configurations of balls placed inside bins, obeying certain transition rules. We prove that we can couple the behaviour of any finite number of balls, provided at least two different transition rules are allowed. This coupling makes it possible to define the regeneration events needed by Foss and Zachary to prove convergence results for the distribution of the balls.