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. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010

Bertoin, J; Sidoravicius, V; Vares, M E (2010). *A system of grabbing particles related to Galton-Watson trees.* Random Structures & Algorithms, 36(4):477-487.

## 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. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | random tree; random graphs; branching process; particle system; polymerization |

Language: | English |

Date: | 2010 |

Deposited On: | 25 Apr 2013 10:01 |

Last Modified: | 05 Apr 2016 16:44 |

Publisher: | John Wiley & Sons, Inc. |

ISSN: | 1098-2418 |

Publisher DOI: | https://doi.org/10.1002/rsa.20310 |

Related URLs: | http://arxiv.org/abs/0804.0726 |

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