2015/09/08 by Abraham, Romain, Aymen Bouaziz, Bouaziz, Aymen +2
Mathematics · #FOS: Mathematics #Limits and Structures in Graph Theory #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.1509.02350
openalex publication_date 2015/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.