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Article Dans Une Revue Methodology and Computing in Applied Probability Année : 2004

Convergence of the Marcus-Lushnikov Process

Résumé

The Smoluchowski coagulation equation describes the concentration c(t,x) of particles of mass x>0 at the instant t, in an infinite system of coalescing particles. It is well-known that in some cases, gelation occurs: a particle with infinite mass appears. But this infinite particle is inert, in the sense that it does not interact with finite particles. We consider the so-called Marcus-Lushnikov process, which is a stochastic finite system of coalescing particles. This process is expected to converge, as the number of particles tends to infinity, to a solution of the Smoluchowski coagulation equation. We show that it actually converges to a modified Smoluchowski equation, which takes into account a possible interaction between finite and infinite particles.
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Dates et versions

hal-00149187 , version 1 (24-05-2007)

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  • HAL Id : hal-00149187 , version 1

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Nicolas Fournier, Jean-Sébastien Giet. Convergence of the Marcus-Lushnikov Process. Methodology and Computing in Applied Probability, 2004, pp.219-231. ⟨hal-00149187⟩
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