Critical trees are neither too short nor too fat

Fuente: arXiv
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Autori principali: Addario-Berry, Louigi, Donderwinkel, Serte, Kortchemski, Igor
Natura: Preprint
Pubblicazione: 2023
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author Addario-Berry, Louigi
Donderwinkel, Serte
Kortchemski, Igor
author_facet Addario-Berry, Louigi
Donderwinkel, Serte
Kortchemski, Igor
contents We establish lower tail bounds for the height, and upper tail bounds for the width, of critical size-conditioned Bienaymé 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 Bienaymé trees.
format Preprint
id arxiv_https___arxiv_org_abs_2311_06163
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Critical trees are neither too short nor too fat
Addario-Berry, Louigi
Donderwinkel, Serte
Kortchemski, Igor
Probability
Combinatorics
05C05, 60C05, 60J80
We establish lower tail bounds for the height, and upper tail bounds for the width, of critical size-conditioned Bienaymé 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 Bienaymé trees.
title Critical trees are neither too short nor too fat
topic Probability
Combinatorics
05C05, 60C05, 60J80
url https://arxiv.org/abs/2311.06163