Geodesic
Limit theorems for the number of trees of a~given size in a~random forest
Sbornik. Mathematics, Tome 32 (1977) no. 3, pp. 335-345

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The author considers the set of all forests consisting of $N$ rooted trees and containing $n$ nonroot vertices; the root vertices are numbered from 1 to $N$, and the nonroot from 1 to $n$. A uniform probability distribution is introduced on this set. Let $\mu_r(n,N)$ denote a random variable equal to the number of trees of a random forest containing exactly $r$ nonroot vertices. Results are obtained yielding a complete description of the limit behavior of the variables $\mu_r(n,N)$ for all values of $r$ for various ways of letting $n$ and $N$ approach infinity. It is shown that these results can be used for studying random mappings. Bibliography: 9 titles. 
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     author = {Yu. L. Pavlov},
     title = {Limit theorems for the number of trees of a~given size in a~random forest},
     journal = {Sbornik. Mathematics},
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     year = {1977},
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     url = {http://geodesic.mathdoc.fr/item/SM_1977_32_3_a4/}
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Yu. L. Pavlov. Limit theorems for the number of trees of a~given size in a~random forest. Sbornik. Mathematics, Tome 32 (1977) no. 3, pp. 335-345. http://geodesic.mathdoc.fr/item/SM_1977_32_3_a4/