A system of grabbing particles related to Galton‐Watson trees |
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| Authors: | Jean Bertoin Vladas Sidoravicius Maria Eulalia Vares |
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| Institution: | 1. Laboratoire de Probabilités, Université Pierre et Marie Curie, 175 rue du Chevaleret, Paris, 75013;2. Département de Mathématiques et Applications, Ecole Normale Supérieure, 45 rue d'Ulm, 75230 Paris Cedex 05, France;3. Instituto Nacional de Matemática Pura e Aplicada, Estr. Dona Castorina 110, Rio de Janeiro, Brasil;4. Centrum Wiskunde & Informatica, Kruislaan 413, 1098 SJ P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;5. Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud, 150. 22290‐180 Rio de Janeiro, RJ. Brasil |
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| 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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| Keywords: | random tree random graphs branching process particle system polymerization |
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