Transactions of KarRC RAS :: Scientific publications

Е.С. Берникович.

О числе деревьев заданного объема в случайном непомеченном некорневом лесе

// Труды КарНЦ РАН. No 5. Сер. Математическое моделирование и информационные технологии, вып. 2. 2011. C. 4-9

E.S. Bernikovich. On the number of trees of a given size in a random unlabelled unrooted forest // Transactions of Karelian Research Centre of Russian Academy of Science. No 5. Mathematical Modeling and Information Technologies. 2011. Pp. 4-9

Keywords: random forests, number of trees of a given size, generalized allocation scheme, limit theorems.

We consider the set FN;n of all random forests consisting of N ordered unrooted trees and n unlabelled vertices with uniform probability distribution on this set. We prove limit theorems for the number of trees of a given size in such forest as N; n → &infin 1 so that 1 < n/N ≤ L = 2:0512772:::