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An elementary proof of Hawkes's conjecture on Galton-Watson trees.


 
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1. Title Title of document An elementary proof of Hawkes's conjecture on Galton-Watson trees.
 
2. Creator Author's name, affiliation, country Thomas S.A. Duquesne; University Paris 6
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Galton-Watson tree; exact Hausdorff measure; boundary; branching measure; size-biased tree
 
3. Subject Subject classification 60J80; 28A78
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR-08-BLAN-0190
 
7. Date (YYYY-MM-DD) 2009-04-19
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1454
 
10. Identifier Digital Object Identifier 10.1214/ECP.v14-1454
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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