Balls-in-boxes duality for coalescing random walks and coalescing Brownian motions

TL;DR

This paper establishes duality relations for coalescing random walks and Brownian motions, extending previous work and applying these results to systems with Poisson immigration.

Contribution

It introduces new duality relations for coalescing processes and applies them to systems with immigration, advancing theoretical understanding.

Findings

Duality relations for coalescing random walks and Brownian motions

Extension of previous duality results in the literature

Application to systems with Poisson immigration

Abstract

We present a duality relation between two systems of coalescing random walks and an analogous duality relation between two systems of coalescing Brownian motions. Our results extends previous work in the literature and we apply it to the study of a system of coalescing Brownian motions with Poisson immigration.