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Павлов Ю.Л.
Еще раз об объемах деревьев леса Гальтона–Ватсона
// Труды КарНЦ РАН. No 6. Сер. Математическое моделирование и информационные технологии. 2026. C. 73-81
Pavlov Yu.L. Once again on the sizes of trees in the Galton – Watson forest // Transactions of Karelian Research Centre of Russian Academy of Science. No 6. Mathematical Modeling and Information Technologies. 2026. Pp. 73-81
Keywords: Galton –Watson forest; tree size; limit theorems; number of trees of a given size
Galton –Watson forests with N rooted trees and n nonroot vertices are considered. It is assumed that such forests are formed by a critical branching process in which the number of offsprings for each particle has the distribution
pk = h(k + 1)/(k + 1)τ, k=0, 1, 2, . . . , τ ∈ (2, 3), where the function h(x) is slowly varying at infinity. Some limit distributions of the number of trees of a given size are found if N, n→∞, n/N →∞.
pk = h(k + 1)/(k + 1)τ, k=0, 1, 2, . . . , τ ∈ (2, 3), where the function h(x) is slowly varying at infinity. Some limit distributions of the number of trees of a given size are found if N, n→∞, n/N →∞.
DOI: 10.17076/mat2296
Indexed at RSCI, RSCI (WS)
Last modified: July 3, 2026