Scaling limit of trees with vertices of fixed degrees and heights
Probability
2026-03-06 v3
Abstract
We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalized converge. To this end, we study the paths from random vertices to the root using coalescent processes. As an application, we obtain scaling limits of Bienaym\'e-Galton-Watson trees in varying environment.
Cite
@article{arxiv.2409.12897,
title = {Scaling limit of trees with vertices of fixed degrees and heights},
author = {Arthur Blanc-Renaudie and Emmanuel Kammerer},
journal= {arXiv preprint arXiv:2409.12897},
year = {2026}
}
Comments
35 pages, 3 figures. To appear in the Annales Henri Lebesgue