|
This article is cited in 2 scientific papers (total in 2 papers)
On the maximal size of tree in a random forest
Yu. L. Pavlov Institute of Applied Mathematical Research of the Karelian Research Centre RAS, Petrozavodsk
Abstract:
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.
Received: 05.06.2022
Citation:
Yu. L. Pavlov, “On the maximal size of tree in a random forest”, Diskr. Mat., 34:4 (2022), 69–83; Discrete Math. Appl., 34:4 (2024), 221–232
Linking options:
https://www.mathnet.ru/eng/dm1729https://doi.org/10.4213/dm1729 https://www.mathnet.ru/eng/dm/v34/i4/p69
|
Statistics & downloads: |
Abstract page: | 277 | Full-text PDF : | 65 | References: | 74 | First page: | 12 |
|