An infinite stochastic model of social network formation

T.M. Liggett, S.W.W. Rolles

    Research output: Contribution to journalArticleAcademicpeer-review

    10 Citations (Scopus)


    We consider an infinite interacting particle system in which 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. We characterize 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.
    Original languageEnglish
    Pages (from-to)65-80
    JournalStochastic Processes and their Applications
    Issue number1
    Publication statusPublished - 2004


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