An Elementary Proof of Hawkes's Conjecture on Galton-Watson Trees

Simple item page
dc.creatorDuquesne, Thomas
dc.date2008-11-12
dc.date.accessioned2026-07-07T10:17:45Z
dc.date.available2026-07-07T10:17:45Z
dc.descriptionIn 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 the infinity of the total mass of the branching measure. Hawkes's conjecture has been proved by T. Watanabe in 2007 as well as other 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.
dc.identifierhttps://arxiv.org/abs/0811.1935
dc.identifierhttp://arxiv.org/abs/0811.1935
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173959
dc.subjectProbability
dc.subject60J80; 28A78
dc.titleAn Elementary Proof of Hawkes's Conjecture on Galton-Watson Trees
dc.typetext

Files

Collections

arXiv