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arXiv · 2311.06163

Critical trees are neither too short nor too fat

Louigi Addario-Berry·Serte Donderwinkel·Igor Kortchemski
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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.

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Louigi Addario-Berry, Serte Donderwinkel, Igor Kortchemski. 2023-11-10. Critical trees are neither too short nor too fat. https://arxiv.org/abs/2311.06163

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