Sub-exponential tail bounds for conditioned stable Bienaymé–Galton–Watson trees

Igor Kortchemski

doi:10.1007/s00440-016-0704-6

Sub-exponential tail bounds for conditioned stable Bienaymé–Galton–Watson trees

Igor Kortchemski

Research output: Contribution to journal › Article › peer-review

Abstract

We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaymé–Galton–Watson trees conditioned on having a large fixed size, whose offspring distribution belongs to the domain of attraction of a stable law. This extends results obtained for the height and width by Addario-Berry, Devroye and Janson in the finite variance case.

Original language	English
Pages (from-to)	1-40
Number of pages	40
Journal	Probability Theory and Related Fields
Volume	168
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-016-0704-6
Publication status	Published - 1 Jun 2017

Keywords

Bienaymé–Galton–Watson trees
Non-crossing trees
Random trees
Spectrally positive stable Lévy processes

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10.1007/s00440-016-0704-6

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title = "Sub-exponential tail bounds for conditioned stable Bienaym{\'e}–Galton–Watson trees",

abstract = "We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaym{\'e}–Galton–Watson trees conditioned on having a large fixed size, whose offspring distribution belongs to the domain of attraction of a stable law. This extends results obtained for the height and width by Addario-Berry, Devroye and Janson in the finite variance case.",

keywords = "Bienaym{\'e}–Galton–Watson trees, Non-crossing trees, Random trees, Spectrally positive stable L{\'e}vy processes",

author = "Igor Kortchemski",

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AU - Kortchemski, Igor

PY - 2017/6/1

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N2 - We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaymé–Galton–Watson trees conditioned on having a large fixed size, whose offspring distribution belongs to the domain of attraction of a stable law. This extends results obtained for the height and width by Addario-Berry, Devroye and Janson in the finite variance case.

AB - We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaymé–Galton–Watson trees conditioned on having a large fixed size, whose offspring distribution belongs to the domain of attraction of a stable law. This extends results obtained for the height and width by Addario-Berry, Devroye and Janson in the finite variance case.

KW - Bienaymé–Galton–Watson trees

KW - Non-crossing trees

KW - Random trees

KW - Spectrally positive stable Lévy processes

U2 - 10.1007/s00440-016-0704-6

DO - 10.1007/s00440-016-0704-6

M3 - Article

AN - SCOPUS:84963650470

SN - 0178-8051

VL - 168

SP - 1

EP - 40

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1-2

ER -

Sub-exponential tail bounds for conditioned stable Bienaymé–Galton–Watson trees

Abstract

Keywords

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