Abstract: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 $$2+\epsilon $$
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