On the Limit Distribution of the Number of Vertices in the Levels of a Galton–Watson Tree

Galton–Watson trees formed by a critical branching process are considered. The distribution of the number of offspring of the particles in the process has infinite variance. The limit distribution of the number of vertices in the lower layers of a tree is found as the number of vertices approaches infinity.

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Publication Details

Journal
Mathematical Notes
Published
2024-10-01
DOI
https://doi.org/10.1134/s0001434624090104
Primary Topic
Stochastic processes and statistical mechanics
Type
article
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article

On the Limit Distribution of the Number of Vertices in the Levels of a Galton–Watson Tree

Yu. L. Pavlov
Mathematical Notes
Stochastic processes and statistical mechanics
article

On the Limit Distribution of the Number of Vertices in the Levels of a Galton–Watson Tree

Yu. L. Pavlov
article en

Abstract

Galton–Watson trees formed by a critical branching process are considered. The distribution of the number of offspring of the particles in the process has infinite variance. The limit distribution of the number of vertices in the lower layers of a tree is found as the number of vertices approaches infinity.

Mathematical NotesVol. 116(3-4)
Karelian Research Centre (RU)
Openalex Percentile: Top 60%
Stochastic processes and statistical mechanics
DOISourceOpenAlex
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On the Limit Distribution of the Number of Vertices in the Levels of a Galton–Watson Tree — Yu. L. Pavlov · Mathematical Notes (2024) | TGRS Research Map | TGRS