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Article Dans Une Revue Electronic Journal of Probability Année : 2014

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

Résumé

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.
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Dates et versions

hal-00813145 , version 1 (15-04-2013)
hal-00813145 , version 2 (28-08-2013)
hal-00813145 , version 3 (10-09-2013)
hal-00813145 , version 4 (16-10-2013)

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Romain Abraham, Jean-François Delmas. Local limits of conditioned Galton-Watson trees: the infinite spine case.. Electronic Journal of Probability, 2014, 19, Article 2, pp 1-19. ⟨10.1214/EJP.v19-2747⟩. ⟨hal-00813145v4⟩
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