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标题：A note on the scaling limits of contour functions of Galton-Watson trees
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作者：He, Hui ; Luan, Nana
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2013
卷号：18
页码：1-13
DOI：10.1214/ECP.v18-2781
语种：English
出版社：Electronic Communications in Probability
摘要：Recently, Abraham and Delmas constructed the distributions of super-critical Lévy trees truncated at a fixed height by connecting super-critical Lévy trees to (sub)critical Lévy trees via a martingale transformation. A similar relationship also holds for discrete Galton-Watson trees. In this work, using the existing works on the convergence of contour functions of (sub)critical trees, we prove that the contour functions of truncated super critical Galton-Watson trees converge weakly to the distributions constructed by Abraham and Delmas.
关键词：Galton-Watson trees; Branching processes; L\'evy trees; contour functions; scaling limit;60J80