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

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

Abstract

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.

Original language	English
Pages (from-to)	757-788
Number of pages	32
Journal	Journal of Theoretical Probability
Volume	31
Issue number	2
DOIs	https://doi.org/10.1007/s10959-016-0739-8
Publication status	Published - 1 Jun 2018

Keywords

Branching process
Galton–Watson tree
Local limit
Random tree
Strong ratio theorem

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10.1007/s10959-016-0739-8

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title = "Critical Multi-type Galton–Watson Trees Conditioned to be Large",

abstract = "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{\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–Watson tree, Local limit, Random tree, Strong ratio theorem",

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

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York.",

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

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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

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DO - 10.1007/s10959-016-0739-8

M3 - Article

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SN - 0894-9840

VL - 31

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

Abstract

Keywords

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