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An infinite stochastic model of social network formation. (English) Zbl 1071.60097
An infinite interacting particle system coming from social network is studied. In the system, individuals choose neighbors according to evolving sets of probabilities. If $$x$$ chooses $$y$$ at some time, the effect is to increase the probability that $$y$$ chooses $$x$$ at later times. The main result of the paper is a characterization of the extremal invariant measures for this process. In an extremal equilibrium, the set of individuals is partitioned into finite sets called stars, each of which includes a “center” that is always chosen by the other individuals in that set. It is remarkable that the extremal equilibrium for this system has a nontrivial structure and is not so easy to observe.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J27 Continuous-time Markov processes on discrete state spaces 82C22 Interacting particle systems in time-dependent statistical mechanics 91D30 Social networks; opinion dynamics
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##### References:
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