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This article is cited in 12 scientific papers (total in 12 papers)
Limit theorems for the number of trees of a given size in a random forest
Yu. L. Pavlov
Abstract:
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.
Received: 12.01.1977
Citation:
Yu. L. Pavlov, “Limit theorems for the number of trees of a given size in a random forest”, Mat. Sb. (N.S.), 103(145):3(7) (1977), 392–403; Math. USSR-Sb., 32:3 (1977), 335–345
Linking options:
https://www.mathnet.ru/eng/sm2913https://doi.org/10.1070/SM1977v032n03ABEH002390 https://www.mathnet.ru/eng/sm/v145/i3/p392
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Abstract page: | 342 | Russian version PDF: | 104 | English version PDF: | 6 | References: | 39 |
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