He, Hui; Luan, Nana A note on the scaling limits of contour functions of Galton-Watson trees. (English) Zbl 1307.60119 Electron. Commun. Probab. 18, Paper No. 79, 13 p. (2013). Summary: Recently, R. Abraham and J.-François Delmas [Ann. Probab. 40, No. 3, 1167–1211 (2012; Zbl 1252.60072)] 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 [loc. cit.]. MSC: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60G51 Processes with independent increments; Lévy processes Keywords:Galton-Watson trees; branching processes; Lévy trees; contour functions; scaling limit Citations:Zbl 1252.60072 PDFBibTeX XMLCite \textit{H. He} and \textit{N. Luan}, Electron. Commun. Probab. 18, Paper No. 79, 13 p. (2013; Zbl 1307.60119) Full Text: DOI arXiv