Growth of Lévy trees

DOI10.1007/s00440-007-0064-3zbMath1126.60068arXivmath/0509518OpenAlexW2041171497MaRDI QIDQ2642933

Matthias Winkel, Thomas S. A. Duquesne

Publication date: 6 September 2007

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509518

zbMATH Keywords

percolationcontinuum random treetree-valued Markov processGalton-Watson branching processreal treeedge lengths

Mathematics Subject Classification ID

Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Cites Work

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• The continuum random tree. I
• Superprocesses and projective limits of branching Markov process
• Rayleigh processes, real trees, and root growth with re-grafting
• Uniqueness for the signature of a path of bounded variation and the reduced path group
• 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)
• 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
• Tree-valued Markov chains derived from Galton-Watson processes
• Branching processes in Lévy processes: The exploration process
• Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses
• Snakes and spiders: Brownian motion on \(\mathbb{R}\)-trees
• Probabilistic and fractal aspects of Lévy trees
• \(T\)-theory: An overview
• The real tree
• Growth of the Brownian forest
• Combinatorial stochastic processes. Ecole d'Eté de Probabilités de Saint-Flour XXXII -- 2002.
• Subtree prune and regraft: a reversible real tree-valued Markov process
• Probability on Trees and Networks
• The shape of large Galton-Watson trees with possibly infinite variance
• Cutting Markovian trees
• Weighted Occupation Time for Branching Particle Systems and a Representation for the Supercritical Superprocess
• 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