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

Romain Abraham; Aymen Bouaziz; Jean-François Delmas

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arXiv · 1509.02350

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

Romain Abraham·Aymen Bouaziz·Jean-François Delmas

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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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Romain Abraham, Aymen Bouaziz, Jean-François Delmas. 2015-09-08. Local limits of galton-watson trees conditioned on the number of protected nodes. https://arxiv.org/abs/1509.02350

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