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A system of grabbing particles related to Galton-Watson trees


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

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
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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