Large conditioned Galton-Watson trees and plane noncrossing configurations
type: Dataset
description: Scaling limits of large random trees play an important role in this thesis. We are more precisely interested in the asymptotic behavior of several functions coding conditioned Galton-Watson trees. We consider several types of conditioning, involving different quantities such as the total number of vertices or leaves, as well as several types of offspring distributions. When the offspring distribution is critical and belongs to the domainof attraction of a stable law, a universality phenomenon occurs: these trees look like the samecontinuous random tree, the so-called stable Lévy tree. However, when the offspring distributionis not critical, the theoretical physics community has noticed that condensation phenomenamay occur, meaning that with high probability there exists a unique vertex with macroscopicdegree comparable to the total size of the tree. The goal of one of our contributions is to graspa better understanding of this phenomenon. Last but not least, we study random non-crossingconfigurations consisting of diagonals of regular polygons, and notice that they are intimatelyrelated to Galton-Watson trees conditioned on having a fixed number of leaves. In particular,this link sheds new light on uniform dissections and allows us to obtain some interesting resultsof a combinatorial flavor.
landing page: https://theses.hal.science/tel-00818190
identifier: NNT: 2012PA112362
keyword: arbres-aleatoires
keyword: arbres-de-galton-watson-conditionnes
keyword: brownian-triangulation
keyword: condensation
keyword: conditioned-galton-watson-trees
keyword: dissections-aleatoires
keyword: infoeu-reposemanticsdoctoralthesis
keyword: limites-dechelle
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: processus-de-levy-stable
keyword: random-dissections
keyword: random-trees
keyword: scaling-limits
keyword: stable-levy-process
keyword: theses
keyword: triangulation-brownienne
issued: 2026-05-11T07:31:09.776096
modified: 2026-05-11T07:31:09.776101
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Large conditioned Galton-Watson trees and plane noncrossing configurations
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00818190
issued: 2026-05-11T07:31:09.788310
modified: 2026-05-11T07:31:09.756881