On the maximal size of tree in a random forest
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Yuriy L. Pavlov
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 → ∞ in such a way that n/N → ∞. Our conditions are significantly wider than was previously known.
Originally published in Diskretnaya Matematika (2022) 34, №4, 69–83 (in Russian).
Funding statement: The work was carried out with the support of Federal budget funds for the implementation of the State assignment for the KarRC RAS (Institute of Applied Mathematical Research of the Karelian Research Centre RAS).
References
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Articles in the same Issue
- Frontmatter
- On large deviations of the moment of attaining far level by the random walk in a random environment
- Asymptotic local lower deviations of strictly supercritical branching process in a random environment with geometric distributions of descendants
- Cloning operations and graph diameter
- Relations between energy complexity measures of Boolean networks and positive sensitivity of Boolean functions
- On the maximal size of tree in a random forest
- Deciding multiaffinity of polynomials over a finite field
- Probability that given vertices belong to the same connected component of random equiprobable mapping
Articles in the same Issue
- Frontmatter
- On large deviations of the moment of attaining far level by the random walk in a random environment
- Asymptotic local lower deviations of strictly supercritical branching process in a random environment with geometric distributions of descendants
- Cloning operations and graph diameter
- Relations between energy complexity measures of Boolean networks and positive sensitivity of Boolean functions
- On the maximal size of tree in a random forest
- Deciding multiaffinity of polynomials over a finite field
- Probability that given vertices belong to the same connected component of random equiprobable mapping
