Limits of biconditioned Bienayme-Galton-Watson trees

Fuente: arXiv
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Autor principal: Dan, Vanessa
Formato: Preprint
Publicado: 2025
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author Dan, Vanessa
author_facet Dan, Vanessa
contents We study the limiting behavior of a Bienayme-Galton-Watson tree conditioned to have a large number of vertices and either a fixed number of leaves or a fixed number of internal nodes. The first biconditioning gives a universal result with respect to the offspring distribution. In contrast, the second case leads to a variety of limiting behaviors, ranging from condensation phenomena to more elongated tree structures, depending on the properties of the offspring distribution. To prove these results, we use tools from conditioned random walk theory and from analytic combinatorics.
format Preprint
id arxiv_https___arxiv_org_abs_2507_22135
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Limits of biconditioned Bienayme-Galton-Watson trees
Dan, Vanessa
Probability
Combinatorics
We study the limiting behavior of a Bienayme-Galton-Watson tree conditioned to have a large number of vertices and either a fixed number of leaves or a fixed number of internal nodes. The first biconditioning gives a universal result with respect to the offspring distribution. In contrast, the second case leads to a variety of limiting behaviors, ranging from condensation phenomena to more elongated tree structures, depending on the properties of the offspring distribution. To prove these results, we use tools from conditioned random walk theory and from analytic combinatorics.
title Limits of biconditioned Bienayme-Galton-Watson trees
topic Probability
Combinatorics
url https://arxiv.org/abs/2507.22135