A system of grabbing particles related to Galton-Watson trees
Probability
2009-06-04 v2
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.
Keywords
Cite
@article{arxiv.0804.0726,
title = {A system of grabbing particles related to Galton-Watson trees},
author = {Jean Bertoin and Vladas Sidoravicius and Maria Eulalia Vares},
journal= {arXiv preprint arXiv:0804.0726},
year = {2009}
}