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Pré-Publication, Document De Travail Année : 2009

A system of grabbing particles related to Galton-Watson trees

Résumé

We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a particle has been grabbed then it cannot be grabbed again, and an arm cannot grab a particle that belongs to its own cluster. We are interested in the shape of a typical polymer in the situation when the initial number of monomers is large and the numbers of arms of monomers are given by i.i.d. random variables. Our main result is a limit theorem for the empirical distribution of polymers, where limit is expressed in terms of a Galton-Watson tree.
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Dates et versions

hal-00270344 , version 1 (04-04-2008)
hal-00270344 , version 2 (04-06-2009)

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Jean Bertoin, Vladas Sidoravicius, Maria Eulalia Vares. A system of grabbing particles related to Galton-Watson trees. 2009. ⟨hal-00270344v2⟩
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