Scientific publications

Хворостянская Е.В.

Предельные теоремы для максимального объема дерева в лесе Гальтона - Ватсона с ограниченным числом вершин

// Труды КарНЦ РАН. No 4. Сер. Математическое моделирование и информационные технологии. 2025. C. 65-73

Khvorostyanskaya E.V. Limit theorems for the maximum tree size in the Galton –Watson forest with a bounded number of vertices // Transactions of Karelian Research Centre of Russian Academy of Science. No 4. Mathematical Modeling and Information Technologies. 2025. Pp. 65-73

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

We consider a random forest formed by trajectories of a homogeneous Galton – Watson branching process starting with N particles, where the number of immediate offspring of each particle has the distribution pk = (k + 1)^−τ − (k + 2)^−τ, k = 0,1,2,... . For the Galton –Watson forest containing at most n vertices, we find limit distributions of the maximum tree size as N, n→∞ for different values of the parameter τ corresponding to a critical or subcritical branching process.

URL: http://journals.krc.karelia.ru/index.php/mathem/article/view/2097

DOI: 10.17076/mat2097

Indexed at RSCI, RSCI (WS)

Last modified: June 28, 2025