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A note on the scaling limits of contour functions of Galton-Watson trees. (English) Zbl 1307.60119

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

Citations:

Zbl 1252.60072
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