Limit theorems for the maximal tree size of a Galton – Watson forest in the critical case
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Elena V. Khvorostianskaia
Abstract
We consider a critical Galton – Watson branching process starting with N particles; the number of offsprings is supposed to have the distribution pk=(k + 1)−τ−(k + 2)−τ, k=0, 1, 2, … Limit distributions of the maximal tree size are obtained for the corresponding Galton – Watson forest with N trees and n non-root vertices as N, n → ∞, n/Nτ ⩾ C > 0.
Note
Originally published in Diskretnaya Matematika (2022) 34, №2, 120–136 (in Russian).
Funding statement: The work was carried out with the support of the Federal Budget Fund for the fulfillment of the State Assignment of the KarSC RAS (Institute of Applied Mathematical Research of the KarSC RAS).
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On distance-regular graphs Γ of diameter 3 for which Γ3 is a triangle-free graph
- Limit theorems for the maximal tree size of a Galton – Watson forest in the critical case
- Short complete diagnostic tests for circuits with two additional inputs in some basis
- Nonlinearity of functions over finite fields
- The limit joint distributions of statistics of three tests of the NIST package
- On properties of multiaffine predicates on a finite set
- On the universality of product for classes of linear functions of two variables
Artikel in diesem Heft
- Frontmatter
- On distance-regular graphs Γ of diameter 3 for which Γ3 is a triangle-free graph
- Limit theorems for the maximal tree size of a Galton – Watson forest in the critical case
- Short complete diagnostic tests for circuits with two additional inputs in some basis
- Nonlinearity of functions over finite fields
- The limit joint distributions of statistics of three tests of the NIST package
- On properties of multiaffine predicates on a finite set
- On the universality of product for classes of linear functions of two variables
