期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2017
卷号：XIV
页码：579-611
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We study the conditions for families of fringe or non-fringe subtrees toexist with high probability (whp) in T gwn , a Galton-Walton tree of size n. We rstgive a Poisson approximation of fringe subtree counts in T gwn , which permits usto determine the height of the maximal complete r-ary fringe subtree. Then wedetermine the maximal Kn such that every tree of size at most Kn appears as afringe subtree in T gwn whp. Finally, we show that non-fringe subtree counts areconcentrated and determine, as an application, the height of the maximal completer-ary non-fringe subtree in T gwn .
