Convergence of bi-measure \(\mathbb{R}\)-trees and the pruning process

DOI10.1214/14-AIHP628zbMath1339.60123arXiv1304.6035MaRDI QIDQ902874

Anita Winter, Wolfgang Löhr, Guillaume Voisin

Publication date: 4 January 2016

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.6035

zbMATH Keywords

Galton-Watson treeProhorov metrictree-valued Markov processnon-locally finite measurespointed Gromov-weak topologypruning process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Trees (05C05) Continuous-time Markov processes on general state spaces (60J25) Planar graphs; geometric and topological aspects of graph theory (05C10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (3)

The Aldous chain on cladograms in the diffusion limit ⋮ The gap between Gromov-Vague and Gromov-Hausdorff-vague topology ⋮ Spaces of algebraic measure trees and triangulations of the circle

Cites Work

• Unnamed Item
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• The cut-tree of large Galton-Watson trees and the Brownian CRT
• A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces
• The stable trees are nested
• A continuum-tree-valued Markov process
• Pruning Galton-Watson trees and tree-valued Markov processes
• Marked metric measure spaces
• Pruning a Lévy continuum random tree
• The gap between Gromov-Vague and Gromov-Hausdorff-vague topology
• Equivalence of Gromov-Prohorov- and Gromov's \(\underline{\square}_\lambda\)-metric on the space of metric measure spaces
• The continuum random tree. I
• Rayleigh processes, real trees, and root growth with re-grafting
• Convergence in distribution of random metric measure spaces (\(\Lambda \)-coalescent measure trees)
• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
• Random walks, capacity and percolation on trees
• Tree-valued Markov chains derived from Galton-Watson processes
• The standard additive coalescent
• A limit theorem for the contour process of conditioned Galton-Watson trees
• Self-similar fragmentation derived from the stable tree. I: Splitting at heights
• Self-similar fragmentations derived from the stable tree. II: Splitting at nodes
• Poisson snake and fragmentation
• \(T\)-theory: An overview
• The real tree
• Fires on trees
• Exit times for an increasing Lévy tree-valued process
• The continuum random tree. III
• Probability and real trees. Ecole d'Eté de Probabilités de Saint-Flour XXXV -- 2005. Lecture given at the Saint-Flour probability summer school, July 6--23, 2005.
• Fragmentation associated with Lévy processes using snake
• Subtree prune and regraft: a reversible real tree-valued Markov process
• On convergence determining and separating classes of functions
• Record process on the Continuum Random Tree
• Random Records and Cuttings in Binary Search Trees
• Random cutting and records in deterministic and random trees
• Cutting down very simple trees
• Tessellations of random maps of arbitrary genus
• Real Analysis and Probability
• Dislocation measure of the fragmentation of a general Lévy tree
• Cutting down random trees
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

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