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2 results

  • On a Daley-Kendall model of random rumours

  • B. Pittel
  • Journal:
    Journal of Applied Probability / Volume 27 / Issue 1 / March 1990
    Published online by Cambridge University Press:
    14 July 2016, pp. 14-27
    Print publication:
    March 1990

  • Suppose that a certain population consists of N individuals. One member initially learns a rumour from an outside source, and starts telling it to other members, who continue spreading the information. A knower becomes inactive once he encounters somebody already informed. Daley and Kendall, who initiated the study of this model, conjectured that the number of eventual knowers is asymptotically normal with mean and variance linear in N. Our purpose is to confirm this conjecture.

  • Random contact processes, snowball sampling and factorial series distributions

  • Sven Berg
  • Journal:
    Journal of Applied Probability / Volume 20 / Issue 1 / March 1983
    Published online by Cambridge University Press:
    14 July 2016, pp. 31-46
    Print publication:
    March 1983

  • A contact process first posed as a random mapping problem is discussed together with a model for the spread of a rumour through an archaic telephone system. Snowball sampling and the well-known Reed–Frost chain binomial model are also commented on. Our main interest and emphasis is on distributional properties of discrete-time models. Simple combinatorial arguments are used along with a class of discrete distributions originally proposed for catch–recapture sampling.