Electronic Communications in Probability

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

Hui He and Nana Luan

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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.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 79, 13 pp.

Accepted: 11 October 2013
First available in Project Euclid: 7 June 2016

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Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Galton-Watson trees Branching processes L\'evy trees contour functions scaling limit

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He, Hui; Luan, Nana. A note on the scaling limits of contour functions of Galton-Watson trees. Electron. Commun. Probab. 18 (2013), paper no. 79, 13 pp. doi:10.1214/ECP.v18-2781. https://projecteuclid.org/euclid.ecp/1465315618

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