Two-Parameter Poisson–Dirichlet Measures and Reversible Exchangeable Fragmentation–Coalescence Processes

DOI10.1017/S0963548307008784zbMath1165.60032arXiv0704.3122OpenAlexW2011634302MaRDI QIDQ3545901

Jean Bertoin

Publication date: 11 December 2008

Published in: Combinatorics, Probability and Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.3122

zbMATH Keywords

coagulationfragmentationreversibilityPoisson-Dirichlet distribution

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items (6)

Reversible Markov structures on divisible set partitions ⋮ A hidden Markov model for latent temporal clustering with application to ideological alignment in the U.S. Supreme Court ⋮ Asymptotic results for coalescent processes without proper frequencies and applications to the two-parameter Poisson-Dirichlet coalescent ⋮ Alpha-diversity processes and normalized inverse-Gaussian diffusions ⋮ Some diffusion processes associated with two parameter Poisson-Dirichlet distribution and Dirichlet process ⋮ A Consistent Markov Partition Process Generated from the Paintbox Process

Cites Work

• Size-biased sampling of Poisson point processes and excursions
• The equilibrium behavior of reversible coagulation-fragmentation processes
• The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
• Coalescents with multiple collisions
• A classification of coalescent processes for haploid exchangeable population models
• The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transfor\-mations.
• Compositions of random transpositions
• A Characterization of GEM Distributions
• Reversible coagulation-fragmentation processes and random combinatorial structures: Asymptotics for the number of groups
• Stationary Random Partitions of Positive Integers
• Poisson–Dirichlet and GEM Invariant Distributions for Split-and-Merge Transformations of an Interval Partition
• The general coalescent with asynchronous mergers of ancestral lines
• Random Fragmentation and Coagulation Processes
• Homogeneous fragmentation processes

This page was built for publication: Two-Parameter Poisson–Dirichlet Measures and Reversible Exchangeable Fragmentation–Coalescence Processes