A. N. Timashov
Large deviations for the number of trees of a given size and for the maximum size of a tree in a random forest
We consider the set of all forests consisting of N rooted trees such that the roots (and the corresponding trees) are labelled by the numbers 1, . . . ,N, and the remaining n vertices of the forest are labelled by the numbers 1, . . . ,n. Under the assumption that the uniform distribution is defined on this set and n, N → ∞, we prove local limit theorems for the distributions of the random variables equal to the number of trees of a given size and the maximum size of a tree, which permit to estimate the corresponding local
probabilities with accuracy of known order, including the probability of large deviations.
Discrete Mathematics and Applications, Walter de Gruyter
Print ISSN: 0924-9266
Volume: 16, 12/2006
Pages: 555 - 561
Show full article (external site)
Show all available items of this journal
Search
