LIMIT THEOREMS FOR THE NUMBER OF TREES OF A GIVEN SIZE IN A RANDOM FOREST

The author considers the set of all forests consisting of rooted trees and containing nonroot vertices; the root vertices are numbered from 1 to , and the nonroot from 1 to . A uniform probability distribution is introduced on this set. Let denote a random variable equal to the number of trees of a random forest containing exactly nonroot vertices. Results are obtained yielding a complete description of the limit behavior of the variables for all values of for various ways of letting and approach infinity. It is shown that these results can be used for studying random mappings.Bibliography: 9 titles.