The standard additive coalescent
Open Access
- 1 October 1998
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 26 (4) , 1703-1726
- https://doi.org/10.1214/aop/1022855879
Abstract
Regard an element of the set\Delta := f(x 1 ; x 2 ; : : :) : x 1 x 2 : : : 0;Xix i = 1gas a fragmentation of unit mass into clusters of masses x i . The additivecoalescent of Evans and Pitman (1997) is the \Delta-valued Markov processin which pairs of clusters of masses fx i ; x j g merge into a cluster of massx i +x j at rate x i +x j . They showed that a version (X1(t); \Gamma1 ! t !1) of this process arises as a n !1 weak limit of the process startedat time \Gamma12...Keywords
This publication has 31 references indexed in Scilit:
- Markov snakes and superprocessesProbability Theory and Related Fields, 1995
- The Brownian snake and solutions of Δu=u 2 in a domainProbability Theory and Related Fields, 1995
- Brownian bridge asymptotics for random mappingsRandom Structures & Algorithms, 1994
- The uniform random tree in a Brownian excursionProbability Theory and Related Fields, 1993
- The Continuum Random Tree IIIThe Annals of Probability, 1993
- Size-biased sampling of Poisson point processes and excursionsProbability Theory and Related Fields, 1992
- Brownian Excursions, Trees and Measure-Valued Branching ProcessesThe Annals of Probability, 1991
- Fluctuations in coagulating systems. IIJournal of Statistical Physics, 1987
- Exact solutions for random coagulation processesZeitschrift für Physik B Condensed Matter, 1985
- A case of limit distribution of the maximal volume on a tree in a random forestMathematical Notes, 1979