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Deterministic and Stochastic Models for Coalescence (Aggregation and Coagulation): A Review of the Mean-Field Theory for Probabilists
Open accessAbstract
Consider N particles, which merge into clusters according to the following rule: a cluster of size x and a cluster of size y merge at stochastic rate K(x,y)/N, where K is a specified rate kernel. This Marcus-Lushnikov model of stochastic coalescence and the underlying deterministic approximation given by the Smoluchowski coagulation equations have an extensive scientific literature. Some mathematical literature (Kingman's coalescent in population genetics; component sizes in random graphs) implicitly studies the special cases K(x,y)=1 and K(x,y)=xy. We attempt a wide-ranging survey. General kernels are only now starting to be studied rigorously; so many interesting open problems appear.
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Metadata
- Authors
- Aldous, D. J.
- Venue
- Bernoulli
- Publisher
- JSTOR
- Published
- 1999-02
- Volume
- 5
- Issue
- 1
- Pages
- 3
- ISSN
- 1350-7265 (ISSN-L)
- OpenAlex
- W2057073325
- Cited by
- 662
- References
- 0
- FWCI
- 28.14
- Type
- journal article
- Language
- en
- Open access
- green
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- CoChat. (2026). Citation check: Deterministic and Stochastic Models for Coalescence (Aggregation and Coagulation): A Review of the Mean-Field Theory for Probabilists. https://app.cochat.ai/papers/10.2307/3318611
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- Aldous, D. J. (1999). Deterministic and Stochastic Models for Coalescence (Aggregation and Coagulation): A Review of the Mean-Field Theory for Probabilists. Bernoulli. https://doi.org/10.2307/3318611
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