Local limits of large Galton–Watson trees rerooted at a random vertex - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Local limits of large Galton–Watson trees rerooted at a random vertex

(1)
1
Benedikt Stufler

Abstract

We discuss various forms of convergence of the vicinity of a uniformly at random selected vertex in random simply generated trees, as the size tends to infinity. For the standard case of a critical Galton–Watson tree conditioned to be large the limit is the invariant random sin-tree constructed by Aldous (1991). In the condensation regime, we describe in complete generality the asymptotic local behaviour from a random vertex up to its first ancestor with large degree. Beyond this distinguished ancestor, different behaviour may occur, depending on the branching weights. In a subregime of complete condensation, we obtain convergence toward a novel limit tree, that describes the asymptotic shape of the vicinity of the full path from a random vertex to the root vertex. This includes the case where the offspring distribution follows a power law up to a factor that varies slowly at infinity.
Fichier principal
Vignette du fichier
pointed.pdf (454.06 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

ensl-01408155 , version 1 (03-12-2016)
ensl-01408155 , version 2 (14-02-2018)

Identifiers

Cite

Benedikt Stufler. Local limits of large Galton–Watson trees rerooted at a random vertex. 2018. ⟨ensl-01408155v2⟩

Collections

ENS-LYON INSMI UDL
102 View
141 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More