Rumour Propagation Among Sceptics: The Markovian Case

Esmaeeli, Neda; Sajadi, Farkhondeh Alsadat

doi:10.1007/s13226-020-0488-3

Cited by 2 publications

(4 citation statements)

References 7 publications

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“…However, our novelties are related to the extension of the rumour process to the sceptical one and its mathematical modelling, and especially to the construction of a convenient discrete-time renewal process, which is difficult to define due to the complexity of our model. We also prove that the condition for the rumour process to survive among the sceptics is equivalent to the available condition of surviving among the non-sceptics, which is in line with the results in [9] and [23].…”

Section: Introductionsupporting

confidence: 88%

“….} by Esmaeeli and Sajadi [9], who also prove that the rumour will survive among sceptics under the same conditions as for non-sceptics.…”

Section: Introductionmentioning

confidence: 84%

“…An equivalent version of this model in stochastic geometry is the study of -coverage by random sets when each vertex of should be covered by at least two distinct random sets. The problem of sceptical rumour propagation has recently been studied in the Markovian setup for by Esmaeeli and Sajadi [9], who also prove that the rumour will survive among sceptics under the same conditions as for non-sceptics.…”

Section: Introductionmentioning

confidence: 99%

“…Our model for the investigation of sceptical rumour spread is different from those of [9] and [23], and is an extension of the classical model in [10] such that the information transfers more slowly in our model. Similarly to the previous versions of information transmission, the probability of survival is the first issue.…”

Section: Introductionmentioning

confidence: 99%

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On the probability of rumour survival among sceptics

Esmaeeli

Sajadi

2023

J. Appl. Probab.

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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.

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Section: Introductionsupporting

confidence: 88%

“….} by Esmaeeli and Sajadi [9], who also prove that the rumour will survive among sceptics under the same conditions as for non-sceptics.…”

Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the probability of rumour survival among sceptics

Esmaeeli

Sajadi

2023

J. Appl. Probab.

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How Fast do Rumours Spread?

Roy,

Saha

2024

J Stat Phys

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We study a rumour propagation model along the lines of Lebensztayn and Rodriguez (Stat Probab Lett 78(14):2130–2136, 2008) as a long-range percolation model on $$\mathbb {Z}$$ Z . We begin by showing a sharp phase transition-type behaviour in the sense of exponential decay of the survival time of the rumour cluster in the sub-critical phase. In the super-critical phase, under the assumption that radius of influence r.v. has $$2+\epsilon $$ 2 + ϵ moment finite (for some $$\epsilon >0$$ ϵ > 0 ), we show that the rightmost vertex in the rumour cluster has a deterministic speed in the sense that after appropriate scaling, the location of the rightmost vertex converges a.s. to a deterministic positive constant. Under the assumption that radius of influence r.v. has $$4+\epsilon $$ 4 + ϵ moment finite, we obtain a central limit theorem for appropriately scaled and centered rightmost vertex. Later, we introduce a rumour propagation model with reactivation. For this section, we work with a family of exponentially decaying i.i.d. radius of influence r.v.’s, and we obtain the speed result for the scaled rightmost position of the rumour cluster. Each of these results is novel, in the sense that such properties have never been established before in the context of the rumour propagation model on $$\mathbb {Z}$$ Z , to the best of our knowledge.

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Rumour Propagation Among Sceptics: The Markovian Case

Cited by 2 publications

References 7 publications

On the probability of rumour survival among sceptics

On the probability of rumour survival among sceptics

How Fast do Rumours Spread?

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