On the maximal tree in Galton–Watson forest with infinite variance of the offspring
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Yuriy L. Pavlov
Abstract
Galton-Watson forests formed by a critical branching process starting with N particles are considered. The total number of descendants of the initial particles over all time of evolution is equal to n. Assume that the number of offspring of each particle has the distribution
where the function h(x) is slowly varying at infinity. The limit distribution of the maximum size of a tree is found if N, n → ∞ and there exist α > 0 such that n/Nτ−1+α → ∞.
Originally published in Diskretnaya Matematika (2023) 35, №2, 38–92 (in Russian).
Funding statement: The work was supported by funds from the Federal budget for the implementation of the State assignment to the KarSC RAS (Institute of Applied Mathematical Research KarSC RAS).
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Articles in the same Issue
- Frontmatter
- On the number of particles from a marked set of cells for an analogue of a general allocation scheme
- Scaling of graphs with diameter constraint
- On the maximal tree in Galton–Watson forest with infinite variance of the offspring
- Short tests for contact circuits with similar-type weakly connected faults of contacts
- Large deviations of bisexual branching process in random environment
- Properties of critical branching random walks on the line under non-extinction condition
Articles in the same Issue
- Frontmatter
- On the number of particles from a marked set of cells for an analogue of a general allocation scheme
- Scaling of graphs with diameter constraint
- On the maximal tree in Galton–Watson forest with infinite variance of the offspring
- Short tests for contact circuits with similar-type weakly connected faults of contacts
- Large deviations of bisexual branching process in random environment
- Properties of critical branching random walks on the line under non-extinction condition
