The Metric Coalescent

TL;DR

The paper introduces the Metric Coalescent, a measure-valued Markov process that generalizes the Kingman Coalescent, derived from a social dynamics model, with proven existence and uniqueness on complex measure spaces.

Contribution

It extends the classical Kingman Coalescent to a broader setting and connects it to a social dynamics agent-based model, with rigorous mathematical foundations.

Findings

Introduces the Metric Coalescent as a generalization of Kingman Coalescent.

Establishes existence and uniqueness of the MC on all Borel probability measures.

Derives the MC from a social dynamics agent-based model.

Abstract

The Metric Coalescent (MC) is a measure-valued Markov Process generalizing the classical Kingman Coalescent. We show how the MC arises naturally from a discrete agent based model (Compulsive Gambler) of social dynamics and prove an existence and uniqueness theorem extending the MC to the space of all Borel probability measures on any locally compact Polish space.