Geodesic
On the maximal size of tree in a random forest
Diskretnaya Matematika, Tome 34 (2022) no. 4, pp. 69-83

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Galton-Watson forests consisting of $N$ rooted trees and $n$ non-root vertices are considered. The distribution of the forest is determined by that of critical branching process with infinite variance and regularly varying tail of the progeny distribution. We prove limit theorem for the maximal size of a tree in a forest as $N,n \rightarrow \infty$ in such a way that $n/N \rightarrow \infty$. Our conditions are significantly wider than was previously known.
Keywords: Galton-Watson forest, tree size, vertex degree, limit theorems. 
@article{DM_2022_34_4_a5,
     author = {Yu. L. Pavlov},
     title = {On the maximal size of tree in a random forest},
     journal = {Diskretnaya Matematika},
     pages = {69--83},
     publisher = {mathdoc},
     volume = {34},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2022_34_4_a5/}
}
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Yu. L. Pavlov. On the maximal size of tree in a random forest. Diskretnaya Matematika, Tome 34 (2022) no. 4, pp. 69-83. http://geodesic.mathdoc.fr/item/DM_2022_34_4_a5/