The social network model on infinite graphs

ANNALS OF APPLIED PROBABILITY, pp. 902-935, 2020.

Cited by: 0|Bibtex|Views2|DOI:https://doi.org/10.1214/19-AAP1520
Other Links: academic.microsoft.com

Abstract:

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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