Geodesic
The maximum tree of a~random forest in the configuration graph
Sbornik. Mathematics, Tome 212 (2021) no. 9, pp. 1329-1346

Voir la notice de l'article provenant de la source Math-Net.Ru

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, tree size, limit theorems.
Mots-clés : configuration graph 
@article{SM_2021_212_9_a6,
     author = {Yu. L. Pavlov},
     title = {The maximum tree of a~random forest in the configuration graph},
     journal = {Sbornik. Mathematics},
     pages = {1329--1346},
     publisher = {mathdoc},
     volume = {212},
     number = {9},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2021_212_9_a6/}
}
TY  - JOUR
AU  - Yu. L. Pavlov
TI  - The maximum tree of a~random forest in the configuration graph
JO  - Sbornik. Mathematics
PY  - 2021
SP  - 1329
EP  - 1346
VL  - 212
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2021_212_9_a6/
LA  - en
ID  - SM_2021_212_9_a6
ER  - 
%0 Journal Article
%A Yu. L. Pavlov
%T The maximum tree of a~random forest in the configuration graph
%J Sbornik. Mathematics
%D 2021
%P 1329-1346
%V 212
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2021_212_9_a6/
%G en
%F SM_2021_212_9_a6
Yu. L. Pavlov. The maximum tree of a~random forest in the configuration graph. Sbornik. Mathematics, Tome 212 (2021) no. 9, pp. 1329-1346. http://geodesic.mathdoc.fr/item/SM_2021_212_9_a6/