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The Entrance Boundary of the Multiplicative Coalescent


 
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1. Title Title of document The Entrance Boundary of the Multiplicative Coalescent
 
2. Creator Author's name, affiliation, country David Aldous; University of California, Berkeley
 
2. Creator Author's name, affiliation, country Vlada Limic; University of California, Berkeley
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Markov process, entrance boundary, excursion, Lévy process, random graph, stochastic coalescent, weak convergence.
 
3. Subject Subject classification 60J50, 60J75
 
4. Description Abstract The multiplicative coalescent $X(t)$ is a $l^2$-valued Markov process representing coalescence of clusters of mass, where each pair of clusters merges at rate proportional to product of masses. From random graph asymptotics it is known (Aldous (1997)) that there exists a standard version of this process starting with infinitesimally small clusters at time $- \infty$.

In this paper, stochastic calculus techniques are used to describe all versions $(X(t);- \infty < t < \infty)$ of the multiplicative coalescent. Roughly, an extreme version is specified by translation and scale parameters, and a vector $c \in l^3$ of relative sizes of large clusters at time $- \infty$. Such a version may be characterized in three ways: via its $t \to - \infty$ behavior, via a representation of the marginal distribution $X(t)$ in terms of excursion-lengths of a Lévy-type process, or via a weak limit of processes derived from the standard version via a "coloring" construction.
 
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7. Date (YYYY-MM-DD) 1998-01-19
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/25
 
10. Identifier Digital Object Identifier 10.1214/EJP.v3-25
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 3
 
12. Language English=en en
 
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