The infinite volume limit of Ford's alpha model

TL;DR

This paper proves the existence of a limiting probability measure in Ford's alpha model for phylogenetic trees, showing it concentrates on trees with a single infinite spine and finite outgrowths, advancing understanding of infinite tree structures.

Contribution

It establishes the existence and characterization of the infinite volume limit in Ford's alpha model, a key step in understanding infinite phylogenetic trees.

Findings

Limit measure exists for Ford's alpha model.

Limit measure concentrates on trees with one infinite spine.

Outgrowths are finite, i.i.d.

Abstract

We prove the existence of a limit of the finite volume probability measures generated by tree growth rules in Ford's alpha model of phylogenetic trees. The limiting measure is shown to be concentrated on the set of trees consisting of exactly one infinite spine with finite, identically and independently distributed outgrowths.