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arXiv · 0804.0726

A system of grabbing particles related to Galton-Watson trees

Jean Bertoin·Vladas Sidoravicius·Maria Eulalia Vares
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Abstract

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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Jean Bertoin, Vladas Sidoravicius, Maria Eulalia Vares. 2009-06-04. A system of grabbing particles related to Galton-Watson trees. https://arxiv.org/abs/0804.0726

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