Exchangeable partitions derived from Markovian coalescents with simultaneous multiple collisions

TL;DR

This paper extends the theory of exchangeable partitions to a generalized coalescent model with simultaneous multiple collisions, providing new characterizations and recursion formulas.

Contribution

It introduces a novel framework for exchangeable partitions derived from coalescents with simultaneous multiple collisions, generalizing previous models.

Findings

Derived recursion formulas for the generalized model

Provided characterizations of the associated exchangeable partitions

Extended the analogy with regenerative composition and partition structures

Abstract

Kingman derived the Ewens sampling formula for random partitions from the genealogy model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process. M\"ohle described the recursion which determines the generalization of the Ewens sampling formula when the lines of descent are governed by a coalescent with multiple collisions. In a recent work by Dong, Gnedin and Pitman, authors exploit an analogy with the theory of regenerative composition and partition structures, and provide various characterizations of the associated exchangeable random partitions. This paper gives parallel results for the further generalized model with lines of descent following a coalescent with simultaneous multiple collisions.