Random recursive trees and preferential attachment trees are random split trees

Svante Janson

Published 2017-06-17Version 1

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.