Uniform attachment with freezing: Scaling limits

Autor:	Bellin, Étienne, Blanc-Renaudie, Arthur, Kammerer, Emmanuel, Kortchemski, Igor
Rok vydání:	2023
Předmět:	Mathematics - Probability 60D05 60F05
Druh dokumentu:	Working Paper
Popis:	We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving vertices cannot be attached to already frozen ones. We identify a phase transition when the number of non-frozen vertices roughly evolves as the total number of vertices to a given power. In particular, we observe a critical regime where the scaling limit is a random compact real tree, closely related to a time non-homogenous Kingman coalescent process identified by Aldous. Interestingly, in this critical regime, a condensation phenomenon can occur. Comment: 34 pages, 8 figures. This is the second part of a project made by the same authors. V3 : Revised version for publication in AIHP
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.00484 Zobrazit plný text záznamu View this record from Arxiv