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2009 An elementary proof of Hawkes's conjecture on Galton-Watson trees.
Thomas Duquesne
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Electron. Commun. Probab. 14: 151-164 (2009). DOI: 10.1214/ECP.v14-1454


In 1981, J. Hawkes conjectured the exact form of the Hausdorff gauge function for the boundary of supercritical Galton-Watson trees under a certain assumption on the tail at infinity of the total mass of the branching measure. Hawkes's conjecture has been proved by T. Watanabe in 2007 as well as other precise results on fractal properties of the boundary of Galton-Watson trees. The goal of this paper is to provide an elementary proof of Hawkes's conjecture under a less restrictive assumption than in T. Watanabe's paper, by use of size-biased Galton-Watson trees introduced by Lyons, Pemantle and Peres in 1995.


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Thomas Duquesne. "An elementary proof of Hawkes's conjecture on Galton-Watson trees.." Electron. Commun. Probab. 14 151 - 164, 2009.


Accepted: 19 April 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60155
MathSciNet: MR2497323
Digital Object Identifier: 10.1214/ECP.v14-1454

Primary: 60J80
Secondary: 28A78

Keywords: Boundary , branching measure , exact Hausdorff measure , Galton-Watson tree , size-biased tree

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