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

Large conditioned Galton-Watson trees and plane noncrossing configurations
type: Dataset
contact point: Organization
  fn: CCSD
keyword: scaling-limits
keyword: processus-de-levy-stable
keyword: random-dissections
keyword: triangulation-brownienne
keyword: infoeu-reposemanticsdoctoralthesis
keyword: dissections-aleatoires
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: brownian-triangulation
keyword: limites-dechelle
keyword: arbres-aleatoires
keyword: arbres-de-galton-watson-conditionnes
keyword: conditioned-galton-watson-trees
keyword: condensation
keyword: random-trees
keyword: stable-levy-process
keyword: theses
landing page: https://theses.hal.science/tel-00818190
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.
identifier: NNT: 2012PA112362
issued: 2026-05-11T07:31:09.776096
language: fr
modified: 2026-05-11T07:31:09.776101

test_moissonnage_selune
type: Agent