This article is cited in 28 papers

The asymptotic distribution of maximum tree size in a random forest

Yu. L. Pavlov

Moscow

Abstract: A random forest containing $N+n$ points, of which $N$ points are roots, is considered. All the points are labelled. The asymptotic distribution of the maximum size of a tree, in such a forest is studied when $n$, $N\to\infty$ so that $n/N\to 0$, $n/N\to \gamma$ ($0<\gamma<\infty$), $n/N\to\infty$ and $n/N^2\to 0$, or $n/N^2\to\mathrm{const}\ne 0$.

Received: 14.02.1976
Revised: 11.01.1977

 English version: Theory of Probability and its Applications, 1978, 22:3, 509–520

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