The Contact Process on Random Graphs and Galton Watson Trees
نویسندگان
چکیده
منابع مشابه
Branching random walks and contact processes on Galton-Watson trees
We consider branching random walks and contact processes on infinite, connected, locally finite graphs whose reproduction and infectivity rates across edges are inversely proportional to vertex degree. We show that when the ambient graph is a Galton-Watson tree then, in certain circumstances, the branching random walks and contact processes will have weak survival phases. We also provide bounds...
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We show that the branching random walk on a Galton–Watson tree may have one or two phase transitions, depending on the relative sizes of the mean degree and the maximum degree. We show that there are some Galton–Watson trees on which the branching random walk has one phase transition while the contact process has two; this contradicts a conjecture of Madras and Schinazi. We show that the contac...
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Each variable X is a new, independent Uniform [0, 1] random number. For example, T = ∅ with probability 1−p, T = (∅, ∅) with probability p(1−p)2, and T = ((∅, ∅), ∅) with probability p2(1− p). The number of vertices N is equal to twice the number of left parentheses (parents) in the expression for T , plus one. Equivalently, N is twice the number of ∅s (leaves), minus one. It can be shown that ...
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ژورنال
عنوان ژورنال: Latin American Journal of Probability and Mathematical Statistics
سال: 2020
ISSN: 1980-0436
DOI: 10.30757/alea.v17-07