WIAS Preprint No. 1037, (2005)

Induced gelation in a two-site spatial coagulation model



Authors

  • Siegmund-Schultze, Rainer
  • Wagner, Wolfgang

2010 Mathematics Subject Classification

  • 60K40

Keywords

  • Spatial coagulation model, induced gelation, stochastic particle systems

Abstract

A two-site spatial coagulation model is considered. Particles of masses $m$ and $n$ at the same site form a new particle of mass $m+n$ at rate $mn,.$ Independently, particles jump to the other site at a constant rate. The limit (for increasing particle numbers) of this model is expected to be non-deterministic after the gelation time, namely, one or two giant particles randomly jump between the two sites. Moreover, a new effect of induced gelation is observed - the gelation happening at the site with the larger initial number of monomers immediately induces gelation at the other site. Induced gelation is shown to be of logarithmic order. The limiting behaviour of the model is derived rigorously up to the gelation time, while the expected post-gelation behaviour is illustrated by a numerical simulation.

Appeared in

  • Ann. Appl. Probab., 16 (2006) pp. 370-402.

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