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Competing first passage percolation on random graphs with finite variance degrees
Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden.
Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2019 (English)In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 55, no 3, p. 545-559Article in journal (Refereed) Published
Abstract [en]

We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph in that an uninfected vertex becomes type 1 (2) infected at rate lambda(1) (lambda(2)) times the number of nearest neighbors of type 1 (2). Assuming (essentially) that the degree of a randomly chosen vertex has finite second moment, we show that if lambda(1) = lambda(2), then the fraction of vertices that are ultimately infected by type 1 converges to a continuous random variable V is an element of (0,1), as the number of vertices tends to infinity. Both infection types hence occupy a positive (random) fraction of the vertices. If lambda(1) not equal lambda(2), on the other hand, then the type with the larger intensity occupies all but a vanishing fraction of the vertices. Our results apply also to a uniformly chosen simple graph with the given degree sequence.

Place, publisher, year, edition, pages
WILEY , 2019. Vol. 55, no 3, p. 545-559
Keywords [en]
coexistence, competing growth, configuration model, continuous-time branching process, first passage percolation, random graphs
National Category
Computer Sciences Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-393719DOI: 10.1002/rsa.20846ISI: 000482128300002OAI: oai:DiVA.org:uu-393719DiVA, id: diva2:1354784
Available from: 2019-09-26 Created: 2019-09-26 Last updated: 2019-09-26Bibliographically approved

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Janson, Svante

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