Scientific publications

Е.В. Хворостянская.

О предельном распределении максимального объема дерева в лесе Гальтона - Ватсона со степенным распределением

// Труды КарНЦ РАН. No 6. Сер. Математическое моделирование и информационные технологии. 2021. C. 64–76

E.V. Khvorostyanskaya. On the limit distribution of the maximum tree size in a Galton – Watson forest with a power-law distribution // Transactions of Karelian Research Centre of Russian Academy of Science. No 6. Mathematical Modeling and Information Technologies. 2021. P. 64–76

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

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

URL: http://journals.krc.karelia.ru/index.php/mathem/article/view/1448

DOI: 10.17076/mat1448

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Last modified: April 11, 2023