Hereditary tree growth and Lévy forests

DOI10.1016/j.spa.2018.10.007zbMath1471.60135arXiv1211.2179OpenAlexW2963779951MaRDI QIDQ2274253

Matthias Winkel, Thomas S. A. Duquesne

Publication date: 19 September 2019

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.2179

zbMATH Keywords

invariance principletightnessGromov-Hausdorff distancelimit theoremsGalton-Watson treeLévy treecontinuous-state branching processreal treeleaf erasure

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Functional limit theorems; invariance principles (60F17)

Related Items (6)

Gromov-Hausdorff-Prokhorov convergence of vertex cut-trees of \(n\)-leaf Galton-Watson trees ⋮ Invariant Galton–Watson trees: metric properties and attraction with respect to generalized dynamical pruning ⋮ Dynamical pruning of rooted trees with applications to 1-D ballistic annihilation ⋮ Exit times for an increasing Lévy tree-valued process ⋮ Invariance and attraction properties of Galton-Watson trees ⋮ Random self-similar trees: a mathematical theory of Horton laws

Cites Work

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• A continuum-tree-valued Markov process
• The continuum random tree. I
• Superprocesses and projective limits of branching Markov process
• Rayleigh processes, real trees, and root growth with re-grafting
• Convergence in distribution of random metric measure spaces (\(\Lambda \)-coalescent measure trees)
• Uniqueness for the signature of a path of bounded variation and the reduced path group
• Williams' decomposition of the Lévy continuum random tree and simultaneous extinction probability for populations with neutral mutations
• Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces
• Arbres et processus de Galton-Watson. (Trees and Galton-Watson processes)
• Subdiffusive behavior of random walk on a random cluster
• Topologie de Gromov équivariante, structures hyperboliques et arbres réels. (Equivariant Gromov topology, hyperbolic structures, and \({\mathbb{R}}\)-trees)
• The Gromov topology on \({\mathbb{R}}\)-trees
• Continuous branching processes and spectral positivity
• On the convergence of sequences of branching processes
• Continuity of a class of random time trnsformations
• Branching processes in Lévy processes: The exploration process
• Snakes and spiders: Brownian motion on \(\mathbb{R}\)-trees
• Probabilistic and fractal aspects of Lévy trees
• On the transition from a Markov chain to a continuous time process
• \(T\)-theory: An overview
• The real tree
• The continuum random tree. III
• Regenerative real trees
• Subtree prune and regraft: a reversible real tree-valued Markov process
• Growth of Lévy trees
• The shape of large Galton-Watson trees with possibly infinite variance
• The Limit of a Sequence of Branching Processes
• Stochastic branching processes with continuous state space
• Continuous state branching processes
• 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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