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  • On the probability of rumour survival among sceptics

  • Part of
  • Neda Esmaeeli, Farkhondeh Alsadat Sajadi
  • Journal:
    Journal of Applied Probability / Volume 60 / Issue 3 / September 2023
    Published online by Cambridge University Press:
    02 March 2023, pp. 1096-1111
    Print publication:
    September 2023
    • Article
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  • We study a sceptical rumour model on the non-negative integer line. The model starts with two spreaders at sites 0, 1 and sceptical ignorants at all other natural numbers. Then each sceptic transmits the rumour, independently, to the individuals within a random distance on its right after s/he receives the rumour from at least two different sources. We say that the process survives if the size of the set of vertices which heard the rumour in this fashion is infinite. We calculate the probability of survival exactly, and obtain some bounds for the tail distribution of the final range of the rumour among sceptics. We also prove that the rumour dies out among non-sceptics and sceptics, under the same condition.