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Local limits of galton-watson trees conditioned on the number of protected nodes

Abstract : We consider a marking procedure of the vertices of a tree where each vertex is marked independently from the others with a probability that depends only on its out-degree. We prove that a critical Galton-Watson tree conditioned on having a large number of marked vertices converges in distribution to the associated size-biased tree. We then apply this result to give the limit in distribution of a critical Galton-Watson tree conditioned on having a large number of protected nodes.
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Submitted on : Monday, April 25, 2016 - 11:42:11 AM
Last modification on : Thursday, May 3, 2018 - 3:32:07 PM
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  • HAL Id : hal-01195701, version 2
  • ARXIV : 1509.02350

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Romain Abraham, Aymen Bouaziz, Jean-François Delmas. Local limits of galton-watson trees conditioned on the number of protected nodes. Journal of Applied Probability, Applied Probability Trust, 2017, 54, pp.55-65. ⟨hal-01195701v2⟩

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