文章基本信息

标题：Simply Generated Unrooted Plane Trees
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作者：Leon Ramzews ; Benedikt Stufler
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：1
页码：333-359
DOI：10.30757/ALEA.v16-12
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We study random unrooted plane trees with n vertices sampled accordingto the weights corresponding to the vertex-degrees. Our main result shows thatif the generating series of the weights has positive radius of convergence, then thismodel of random trees may be approximated geometrically by a Galton{Watsontree conditioned on having a large random size. This implies that a variety ofresults for the well-studied planted case also hold for unrooted trees, includingGromov{Hausdor{Prokhorov scaling limits, tail-bounds for the diameter, distributionalgraph limits, and limits for the maximum degree. Our work complementsresults by Wang (2016), who studied random unrooted plane trees whose diametertends to innity.
关键词：random trees; unrooted plane trees.