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Local limits of conditioned Galton-Watson trees: the infinite spine case


 
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1. Title Title of document Local limits of conditioned Galton-Watson trees: the infinite spine case
 
2. Creator Author's name, affiliation, country Romain Abraham; Université d'Orléans; France
 
2. Creator Author's name, affiliation, country Jean-François Delmas; École Nationale des Ponts et Chaussées Université Paris-Est; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Conditioned Galton-Watson tree, Kesten's tree
 
3. Subject Subject classification 60J80
 
4. Description Abstract We give a necessary and sufficient condition for the convergence in distribution of a conditioned Galton-Watson tree to Kesten's tree. This yields elementary proofs of Kesten's result as well as other known results on local limit of conditioned Galton-Watson trees. We then apply this condition to get new results, in the critical and sub-critical cases, on the limit in distribution of a Galton-Watson tree conditioned on having a  large number of individuals with out-degree in a given set.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2014-01-03
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2747
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-2747
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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