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Rumour Propagation Among Sceptics: The Markovian Case

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Abstract

We consider a model of the spread of rumour among sceptical individuals. Let X0, X1,… be a {0, 1}-valued Markov chain and ρ0, ρ1, … a sequence of i.i.d. ℕ valued random variables independent of the Markov chain. An individual located at site i ∈ ℕ*:= ℕ ∪ {0} spreads the rumour to the individuals located in the interval [i, i + ρi] provided (i) Xi = 1 and (ii) if s/he has received the rumour from at least two distinct sources j, k < i with Xj = Xk = 1. To start the process we place two individuals at locations −1 and −2, each of spread the rumour to a distance ρ−1 and ρ−2 respectively to the right of itself. Here ρ−1 and ρ−2 are i.i.d. copies of ρ0. This extends the work of Sajadi and Roy [7] who considered the case when X0, X1,… is a sequence of i.i.d. {0,1} valued random variables, i.e. the believers {i: Xi = 1} and the disbelievers {i: Xi = 0} are located in an i.i.d. fashion. Here we study the case when the the believers and the disbelievers are located in a Markovian fashion.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran

    Neda Esmaeeli

  2. Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran

    Farkhondeh Alsadat Sajadi

Authors
  1. Neda Esmaeeli
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  2. Farkhondeh Alsadat Sajadi
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Correspondence to Neda Esmaeeli or Farkhondeh Alsadat Sajadi.

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Esmaeeli, N., Sajadi, F.A. Rumour Propagation Among Sceptics: The Markovian Case. Indian J Pure Appl Math 51, 1661–1671 (2020). https://doi.org/10.1007/s13226-020-0488-3

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  • DOI: https://doi.org/10.1007/s13226-020-0488-3

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