The winner takes it all
نویسندگان
چکیده
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 λ1 (λ2) 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 τ ∈ (2, 3), then, as the number of vertices tends to infinity, one of the infection types will almost surely 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 λ1 and λ2. The picture is similar with multiple starting points for the infections.
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