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We extend results about heights of random trees (Devroye, JACM 33 (1986) 489–498 , SIAM J COMP 28 (1998) 409–432) . In this paper, a general split tree model is considered in which the normalized subtree sizes of nodes converge in distribution. The height of these trees is shown to be in probability asymptotic to c log n for some constant c . We apply our results to obtain a law of large numbers for the height of all polynomial varieties of increasing trees (Bergeron et al. Lect Notes Comput Sci (1992) 24–48) .
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Broutin et al. (2008) studied this question.
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