Does freezing impede the growth of random recursive trees?
Probability
2026-05-05 v2
Abstract
Uniform attachment with freezing is an extension of the classical model of random recursive trees, in which trees are recursively built by attaching new vertices to old ones. In the model of uniform attachment with freezing, vertices are allowed to freeze, in the sense that new vertices cannot be attached to already frozen ones. We study the impact of removing attachment and/or freezing steps on the height of the trees. We show in particular that removing an attachment step can increase the expected height, and that freezing cannot substantially decrease the height of random recursive trees. Our methods are based on coupling arguments.
Keywords
Cite
@article{arxiv.2505.16571,
title = {Does freezing impede the growth of random recursive trees?},
author = {Anna Brandenberger and Simon Briend and Hannah Cairns and Robin Khanfir and Igor Kortchemski},
journal= {arXiv preprint arXiv:2505.16571},
year = {2026}
}