Fires on trees

DOI10.1214/11-AIHP435zbMath1263.60083arXiv1011.2308MaRDI QIDQ1930648

Jean Bertoin

Publication date: 11 January 2013

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/1011.2308

zbMATH Keywords

percolationCayley treefire modelgiant component

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Bivariate Markov chains converging to Lamperti transform Markov additive processes ⋮ Two-dimensional volume-frozen percolation: deconcentration and prevalence of mesoscopic clusters ⋮ On moment sequences and mixed Poisson distributions ⋮ Probability, trees and algorithms. Abstracts from the workshop held November 2--8, 2014. ⋮ The cut-tree of large Galton-Watson trees and the Brownian CRT ⋮ Gromov-Hausdorff-Prokhorov convergence of vertex cut-trees of \(n\)-leaf Galton-Watson trees ⋮ Frozen percolation in two dimensions ⋮ A modification of the random cutting model ⋮ Fires on large recursive trees ⋮ A growth-fragmentation-isolation process on random recursive trees and contact tracing ⋮ Scaling Limits of Markov-Branching Trees and Applications ⋮ Convergence of bi-measure \(\mathbb{R}\)-trees and the pruning process ⋮ Cutting Edges at Random in Large Recursive Trees ⋮ Cutting down trees with a Markov chainsaw ⋮ A new combinatorial representation of the additive coalescent ⋮ A planar Ising model of self-organized criticality ⋮ Scaling limits of multi-type Markov branching trees ⋮ Inverting the cut-tree transform ⋮ The cut-tree of large recursive trees ⋮ The vertex-cut-tree of Galton-Watson trees converging to a stable tree

Cites Work

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• The continuum random tree. III
• Random cutting and records in deterministic and random trees
• Cutting down very simple trees
• The Asymptotic Distribution of Maximum Tree Size in a Random Forest
• Random Fragmentation and Coagulation Processes
• Cutting down random trees

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