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Sbornik: Mathematics, 2021, Volume 212, Issue 9, Pages 1329–1346
DOI: https://doi.org/10.1070/SM9481 (Mi sm9481) 		 
This article is cited in 9 scientific papers (total in 9 papers)

The maximum tree of a random forest in the configuration graph

Yu. L. Pavlov

Institute of Applied Mathematical Research, Karelian Research Centre of the Russian Academy of Sciences, Petrozavodsk, Russia
English version PDF (521 kB) Citations (9)
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DOI: https://doi.org/10.1070/SM9481
Abstract: Galton-Watson random forests with a given number of root trees and a known number of nonroot vertices are investigated. The distribution of the number of direct offspring of each particle in the forest-generating process is assumed to have infinite variance. Branching processes of this kind are used successfully to study configuration graphs aimed at simulating the structure and development dynamics of complex communication networks, in particular the internet. The known relationship between configuration graphs and random forests reflects the local tree structure of simulated networks. Limit theorems are proved for the maximum size of a tree in a random forest in all basic zones where the number of trees and the number of vertices tend to infinity.
Bibliography: 14 titles.
Keywords: random forest, configuration graph, tree size, limit theorems.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-03-2020-522
This research was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-03-2020-522).
Received: 21.07.2020 and 28.09.2020
Russian version:
Matematicheskii Sbornik, 2021, Volume 212, Number 9, Pages 146–163
DOI: https://doi.org/10.4213/sm9481
Bibliographic databases:
Document Type: Article
UDC: 519.179.4
PACS: 02.10.Ox
MSC: 60C05
Language: English
Original paper language: Russian
Citation: Yu. L. Pavlov, “The maximum tree of a random forest in the configuration graph”, Mat. Sb., 212:9 (2021), 146–163; Sb. Math., 212:9 (2021), 1329–1346
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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