Limit of trees with fixed degree sequence
Probability
2025-12-23 v2
Abstract
We show, under natural conditions, that uniform rooted trees with fixed degree sequence converge after renormalization toward inhomogeneous continuum random trees (ICRT). We also provide a sharp upper-bound for the tail of their heights. We also extend our results to P-trees, ICRT, and trees with random degree sequence. In passing we confirm a conjecture of Aldous, Miermont, and Pitman stating that L\'evy trees are ICRT with random parameters.
Keywords
Cite
@article{arxiv.2110.03378,
title = {Limit of trees with fixed degree sequence},
author = {Arthur Blanc-Renaudie},
journal= {arXiv preprint arXiv:2110.03378},
year = {2025}
}
Comments
Second version, largely simplified (structure, results, notations, topologies...). The link with L\'evy trees has been reworked and is more explained. A new appendix gives a simple example of application