Eternal additive coalescents and certain bridges with exchangeable increments
type: Item
instance of: scholarly article
title: Eternal additive coalescents and certain bridges with exchangeable increments
zbMATH Open document ID: 1019.60072
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: The author studies the additive coalescent processes, i.e., random processes which describe the evolution of the ranked sequence of masses in a system of clusters in which each pair of clusters, say with masses \(m_i\) and \(m_j,\) merges as a single cluster with mass \(m_i+m_j\) at rate \(\kappa(m_i,m_j)=m_i+m_j,\) independently of the other pairs. Aldous and Pitman have studied the asymptotic behavior of the additive coalescent processes. The author proposes a different and simpler approach to this problem based on partitions of the unit interval induced by certain bridges with exchangeable increments. The connection between additive coalescent and interval partitions is enlightened by an interpretation in terms of an aggregating server system.
reviewed by: Roman Urban
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60G09
zbMATH DE Number: 1905982
zbMATH Keywords: additive coalescent
zbMATH Keywords: fragmentation
zbMATH Keywords: bridge with exchangeable increments
author: Jean Bertoin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1008956333
OpenAlex ID: W1573705578
cites work: Brownian excursions, critical random graphs and the multiplicative coalescent
cites work: Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists
cites work: The entrance boundary of the multiplicative coalescent
cites work: The standard additive coalescent
cites work: Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
cites work: Splitting at the infimum and excursions in half-lines for random walks and Lévy processes
cites work: Clustering statistics for sticky particles with Brownian initial velocity
cites work: A fragmentation process connected to Brownian motion
cites work: Limit distributions and random trees derived from the birthday problem with unequal probabilities
cites work: A Vervaat-like path transformation for the reflected Brownian bridge conditioned on its local time at 0
cites work: Phase transition for Parking blocks, Brownian excursion and coalescence
cites work: Construction of Markovian coalescents
cites work: Q3774629
cites work: Canonical representations and convergence criteria for processes with interchangeable increments
cites work: Path properties of processes with independent and interchangeable increments
cites work: Q4896008
cites work: A relation between Brownian bridge and Brownian excursion
DOI: 10.1214/AOP/1008956333
description: scientific article; zbMATH DE number 1905982