The social network model on infinite graphs
ANNALS OF APPLIED PROBABILITY, pp. 902-935, 2020.
Given an infinite connected regular graph G = (V, E), place at each vertex Poisson(lambda) walkers performing independent lazy simple random walks on G simultaneously. When two walkers visit the same vertex at the same time they are declared to be acquainted. We show that when G is vertex-transitive and amenable, for all lambda > 0 a.s. a...More
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