CRITICAL TREES ARE NEITHER TOO SHORT NOR TOO FAT

Louigi Addario-Berry; Serte Donderwinkel; Igor Kortchemski

doi:10.5802/ahl.231

CRITICAL TREES ARE NEITHER TOO SHORT NOR TOO FAT

Titre traduit de la contribution: LES ARBRES CRITIQUES NE SONT NI TROP COURTS NI TROP GROS

Louigi Addario-Berry
, Serte Donderwinkel
, Igor Kortchemski

McGill University
ICS/University of Groningen
ETH Zurich

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

2 Citations (Scopus)

Résumé

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 height and width a symptotics when the trees’ offspring distributions lie within the domain of attraction of a Cauchy distribution and satisfy a local regularity condition. Finally, we pose some questions on the possible asymptotic behaviours of the height and width of critical size-conditioned Bienaymé trees.

Titre traduit de la contribution	LES ARBRES CRITIQUES NE SONT NI TROP COURTS NI TROP GROS
langue originale	Anglais
Pages (de - à)	113-149
Nombre de pages	37
journal	Annales Henri Lebesgue
Volume	8
Les DOIs	https://doi.org/10.5802/ahl.231
état	Publié - 1 janv. 2025

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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 height and width a symptotics when the trees{\textquoteright} offspring distributions lie within the domain of attraction of a Cauchy distribution and satisfy a local regularity condition. 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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AU - Kortchemski, Igor

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AB - 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 height and width a symptotics when the trees’ offspring distributions lie within the domain of attraction of a Cauchy distribution and satisfy a local regularity condition. Finally, we pose some questions on the possible asymptotic behaviours of the height and width of critical size-conditioned Bienaymé trees.

KW - Cauchy distribution

KW - Random trees

KW - Tail bounds

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JO - Annales Henri Lebesgue

JF - Annales Henri Lebesgue

ER -

CRITICAL TREES ARE NEITHER TOO SHORT NOR TOO FAT

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