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Local limits of galton-watson trees conditioned on the number of protected nodes
- Publication Year :
- 2015
-
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.
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1509.02350
- Document Type :
- Working Paper