A system of grabbing particles related to Galton-Watson trees

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.

• Type: Journal
• Year: 2010
• Where: RSA
• Authors: Jean Bertoin, Vladas Sidoravicius, Maria Eulalia Vares
• Keywords: GRAB, Limit Theorem, RSA 2010, Toy Model