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


 
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1. Title Title of document A note on the scaling limits of contour functions of Galton-Watson trees
 
2. Creator Author's name, affiliation, country Hui He; Beijing Normal University; China
 
2. Creator Author's name, affiliation, country Nana Luan; University of International Business and Economics; China
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Galton-Watson trees; Branching processes; L\'evy trees; contour functions; scaling limit
 
3. Subject Subject classification 60J80
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-10-11
 
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/2781
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2781
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
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