Scaling limit of trees with vertices of fixed degrees and heights
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 Bienaymé–Galton–Watson trees in varying environment.
Fields of Study & Subjects
Graph theory and applications
Stochastic processes and statistical mechanics
Markov Chains and Monte Carlo Methods
Publication details
- Journal / source
- Annales Henri Lebesgue
- Volume
- 9
- Pages
- 423–469
- Publication date
- 12 June 2026
- Language
- EN