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

Hui He (Beijing Normal University)
Nana Luan (University of International Business and Economics)

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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Pages: 1-13

Publication Date: October 11, 2013

DOI: 10.1214/ECP.v18-2781

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