A note on the scaling limits of contour functions of Galton-Watson trees

Hui He; Nana Luan

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arXiv · 1305.1418

A note on the scaling limits of contour functions of Galton-Watson trees

Hui He·Nana Luan

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Abstract

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.

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Hui He, Nana Luan. 2013-05-07. A note on the scaling limits of contour functions of Galton-Watson trees. https://arxiv.org/abs/1305.1418

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