A system of grabbing particles related to Galton-Watson trees

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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Pré-publication, Document de travail
2009
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https://hal.archives-ouvertes.fr/hal-00270344
Contributeur : Jean Bertoin <>
Soumis le : jeudi 4 juin 2009 - 06:35:18
Dernière modification le : jeudi 27 avril 2017 - 09:46:04
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 12:37:19

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  • HAL Id : hal-00270344, version 2
  • ARXIV : 0804.0726

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INSMI | UPMC | PSL | USPC | PMA

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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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