Journal of Applied Probability

Binary trees, exploration processes, and an extended Ray-Knight theorem

Mamadou Ba, Etienne Pardoux, and Ahmadou Bamba Sow

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We study the bijection between binary Galton-Watson trees in continuous time and their exploration process, both in the subcritical and in the supercritical cases. We then take the limit over renormalized quantities, as the size of the population tends to ∞. We thus deduce Delmas' generalization of the second Ray-Knight theorem.

Article information

J. Appl. Probab., Volume 49, Number 1 (2012), 210-225.

First available in Project Euclid: 8 March 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60F17: Functional limit theorems; invariance principles
Secondary: 92D25: Population dynamics (general)

Galton-Watson process Feller's branching exploration process Ray-Knight theorem


Ba, Mamadou; Pardoux, Etienne; Sow, Ahmadou Bamba. Binary trees, exploration processes, and an extended Ray-Knight theorem. J. Appl. Probab. 49 (2012), no. 1, 210--225. doi:10.1239/jap/1331216843.

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