Critical trees are neither too short nor too fat
Probability
2025-03-05 v2 Combinatorics
Abstract
We establish lower tail bounds for the height, and upper tail bounds for the width, of critical size-conditioned Bienaym\'e trees. Our bounds are optimal at this level of generality. We also obtain precise asymptotics for offspring distributions within the domain of attraction of a Cauchy distribution, under a local regularity assumption. Finally, we pose some questions on the possible asymptotic behaviours of the height and width of critical size-conditioned Bienaym\'e trees.
Keywords
Cite
@article{arxiv.2311.06163,
title = {Critical trees are neither too short nor too fat},
author = {Louigi Addario-Berry and Serte Donderwinkel and Igor Kortchemski},
journal= {arXiv preprint arXiv:2311.06163},
year = {2025}
}
Comments
31 pages, 4 figures, revised version to appear in Annales Henri Lebesgue