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THE WINNER TAKES IT ALL
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 2
2016 (English)In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 26, no 4, 2419-2453 p.Article in journal (Refereed) Published
Abstract [en]

We study competing first passage percolation on graphs generated by the configuration model. At time 0, vertex 1 and vertex 2 are infected with the type 1 and the type 2 infection, respectively, and an uninfected vertex then becomes type 1 (2) infected at rate lambda(1) (lambda(2)) times the number of edges connecting it to a type 1 (2) infected neighbor. Our main result is that, if the degree distribution is a power-law with exponent tau is an element of (2, 3), then as the number of vertices tends to infinity and with high probability, one of the infection types will occupy all but a finite number of vertices. Furthermore, which one of the infections wins is random and both infections have a positive probability of winning regardless of the values of lambda(1) and lambda(2). The picture is similar with multiple starting points for the infections.

Place, publisher, year, edition, pages
2016. Vol. 26, no 4, 2419-2453 p.
Keyword [en]
Random graphs, configuration model, first passage percolation, competing growth, coexistence, continuous-time branching process
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-135122DOI: 10.1214/15-AAP1151ISI: 000383411200015OAI: oai:DiVA.org:su-135122DiVA: diva2:1044093
Available from: 2016-11-02 Created: 2016-10-31 Last updated: 2016-11-02Bibliographically approved

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Deijfen, Maria
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