Induced gelation in a two-site spatial coagulation model

Details Induced gelation in a two-site spatial coagulation model Induced gelation in a two-site spatial coagulation model

2006-03-13

arxiv.org/abs/math/0603300v2

Annals of Applied Probability 2006, Vol. 16, No. 1, 370-402

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000755 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000755

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 nondeterministic 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 behavior of the model is derived rigorously up to the gelation time, while the expected post-gelation behavior is illustrated by a numerical simulation.

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