Transactions of KarRC RAS :: Scientific publications

Е.В. Хворостянская.

О предельном распределении максимального объема дерева в лесе Гальтона - Ватсона

// Труды КарНЦ РАН. No 7. Сер. Математическое моделирование и информационные технологии. 2020. C. 89–97

E.V. Khvorostyanskaya. On the limit distribution of the maximum tree size in a Galton-Watson forest // Transactions of Karelian Research Centre of Russian Academy of Science. No 7. Mathematical Modeling and Information Technologies. 2020. P. 89–97

Keywords: Galton – Watson branching process; random forest; maximum tree size; limit distribution

We consider the critical Galton – Watson branching process starting with N particles where the number of direct descendants has a distribution p_k=(k+1)^-τ -(k+2)^-τ, k=0,1,2,… For the corresponding Galton – Watson forest with N trees and n non-root vertices the limit distribution of the maximum tree size is obtained as N,n→∞ such that 0<C₁≤ n/N ≤ C₂<∞.

URL: http://journals.krc.karelia.ru/index.php/mathem/article/view/1236

DOI: 10.17076/mat1236

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