Critical Multi-type Galton–Watson Trees Conditioned to be Large

Romain Abraham; Jean François Delmas; Hongsong Guo

doi:10.1007/s10959-016-0739-8

Critical Multi-type Galton–Watson Trees Conditioned to be Large

Romain Abraham
, Jean François Delmas
, Hongsong Guo

MAPMO
conventionnée avec l'Université d'Orléans
École des ponts
Department of Mathematics
China University of Mining and Technology

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

7 Citations (Scopus)

Résumé

Under minimal condition, we prove the local convergence of a critical multi-type Galton–Watson tree conditioned on having a large total progeny by types toward a multi-type Kesten’s tree. We obtain the result by generalizing Neveu’s strong ratio limit theorem for aperiodic random walks on Z^d.

langue originale	Anglais
Pages (de - à)	757-788
Nombre de pages	32
journal	Journal of Theoretical Probability
Volume	31
Numéro de publication	2
Les DOIs	https://doi.org/10.1007/s10959-016-0739-8
état	Publié - 1 juin 2018

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title = "Critical Multi-type Galton{\textendash}Watson Trees Conditioned to be Large",

abstract = "Under minimal condition, we prove the local convergence of a critical multi-type Galton{\textendash}Watson tree conditioned on having a large total progeny by types toward a multi-type Kesten{\textquoteright}s tree. We obtain the result by generalizing Neveu{\textquoteright}s strong ratio limit theorem for aperiodic random walks on Zd.",

keywords = "Branching process, Galton{\textendash}Watson tree, Local limit, Random tree, Strong ratio theorem",

author = "Romain Abraham and Delmas, \{Jean Fran{\c c}ois\} and Hongsong Guo",

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doi = "10.1007/s10959-016-0739-8",

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T1 - Critical Multi-type Galton–Watson Trees Conditioned to be Large

AU - Abraham, Romain

AU - Delmas, Jean François

AU - Guo, Hongsong

PY - 2018/6/1

Y1 - 2018/6/1

N2 - Under minimal condition, we prove the local convergence of a critical multi-type Galton–Watson tree conditioned on having a large total progeny by types toward a multi-type Kesten’s tree. We obtain the result by generalizing Neveu’s strong ratio limit theorem for aperiodic random walks on Zd.

AB - Under minimal condition, we prove the local convergence of a critical multi-type Galton–Watson tree conditioned on having a large total progeny by types toward a multi-type Kesten’s tree. We obtain the result by generalizing Neveu’s strong ratio limit theorem for aperiodic random walks on Zd.

KW - Branching process

KW - Galton–Watson tree

KW - Local limit

KW - Random tree

KW - Strong ratio theorem

UR - https://www.scopus.com/pages/publications/85008180683

U2 - 10.1007/s10959-016-0739-8

DO - 10.1007/s10959-016-0739-8

M3 - Article

AN - SCOPUS:85008180683

SN - 0894-9840

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SP - 757

EP - 788

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 2

ER -

Critical Multi-type Galton–Watson Trees Conditioned to be Large

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