The standard additive coalescent

DOI10.1214/aop/1022855879zbMath0936.60064OpenAlexW1986567569MaRDI QIDQ1307461

Jim W. Pitman, David J. Aldous

Publication date: 2 December 1999

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1022855879

zbMATH Keywords

Brownian excursionsplittingstochastic fragmentationrandom forestcontinuum random treestable subordinatorstochastic coalescence

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Brownian motion (60J65) Combinatorial probability (60C05)

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Cites Work

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• Unnamed Item
• The continuum random tree. I
• Continuity and weak convergence of ranked and size-biased permutations on the infinite simplex
• A case of limit distribution of the maximal volume of a tree in a random forest
• Brownian excursions, trees and measure-valued branching processes
• Size-biased sampling of Poisson point processes and excursions
• Stopping times and tightness. II
• Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists
• Coalescent random forests
• The uniform random tree in a Brownian excursion
• Recursive self-similarity for random trees, random triangulations and Brownian excursion
• Brownian excursions, critical random graphs and the multiplicative coalescent
• The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
• Partition structures derived from Brownian motion and stable subordinators
• Construction of Markovian coalescents
• Stationary Markov processes related to stable Ornstein-Uhlenbeck processes and the additive coalescent
• Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
• The Brownian snake and solutions of \(\Delta u = u^ 2\) in a domain
• Markov snakes and superprocesses
• The continuum random tree. III
• Order statistics for jumps of normalised subordinators
• Arcsine Laws and Interval Partitions Derived from a Stable Subordinator
• Brownian bridge asymptotics for random mappings
• Random discrete distributions invariant under size-biased permutation
• Conditioned Limit Theorems

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