# Random recursive trees and preferential attachment trees are random split trees

## TL;DR

This paper demonstrates that linear preferential attachment trees, including recursive and standard models, can be viewed as random split trees with infinite branching, providing new insights into their structure and properties.

## Contribution

It establishes a connection between preferential attachment trees and random split trees, extending the concept to infinite potential branching.

## Key findings

- Preferential attachment trees can be modeled as random split trees.
- The approach applies to recursive and standard preferential attachment trees.
- An application to ancestor counting in these trees is provided.

## Abstract

We consider linear preferential attachment trees, and show that they can be regarded as random split trees in the sense of Devroye (1999), although with infinite potential branching. In particular, this applies to the random recursive tree and the standard preferential attachment tree. An application is given to the sum over all pairs of nodes of the common number of ancestors.