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Rumour Propagation Among Sceptics: The Markovian Case
Indian Journal of Pure and Applied Mathematics ( IF 0.7 ) Pub Date : 2021-01-05 , DOI: 10.1007/s13226-020-0488-3
Neda Esmaeeli , Farkhondeh Alsadat Sajadi

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.



中文翻译:

怀疑论者之间的谣言传播:马尔可夫病

我们考虑一个在怀疑者之间传播谣言的模型。让X 0X 1,...为{0,1} -valued马尔可夫链和ρ 0ρ 1,... IIDℕ的序列值独立于Markov链的随机变量。个体位于现场∈ℕ*:=ℕ∪{0}敷于传闻到位于间隔的个体[ I,I + ρ]提供(ⅰ)X= 1和(ii)如果他/她已经从至少两个不同的来源j传言,k <iX j = X k=1。要开始该过程,我们将两个人放置在位置-1和-2处,每个都将谣言散布到其右侧分别距离ρ -1ρ -2处。这里ρ -1ρ -2是独立同分布的副本ρ 0。这扩展了Sajadi和Roy [7]的工作,他们考虑了以下情况:X 0X 1,...是iid {0,1}值随机变量的序列,即信徒{i:X i = 1}和不信者{ iX i= 0}以iid方式定位。在这里,我们研究信徒和不信徒以马尔可夫方式出现的情况。

更新日期:2021-01-05
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