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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Phase Transition for the Maki-Thompson Rumour Model on a Small-World Network

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Author(s):
Agliari, Elena [1] ; Pachon, Angelica [2] ; Rodriguez, Pablo M. [3] ; Tavani, Flavia [1]
Total Authors: 4
Affiliation:
[1] Sapienza Univ Roma, Rome - Italy
[2] Univ Turin, Turin - Italy
[3] Univ Sao Paulo, Sao Carlos, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: Journal of Statistical Physics; v. 169, n. 4, p. 846-875, NOV 2017.
Web of Science Citations: 2
Abstract

We consider the Maki-Thompson model for the stochastic propagation of a rumour within a population. In this model the population is made up of ``spreaders{''}, ``ignorants{''} and ``stiflers{''}; any spreader attempts to pass the rumour to the other individuals via pair-wise interactions and in case the other individual is an ignorant, it becomes a spreader, while in the other two cases the initiating spreader turns into a stifler. In a finite population the process will eventually reach an equilibrium situation where individuals are either stiflers or ignorants. We extend the original hypothesis of homogenously mixed population by allowing for a small-world network embedding the model, in such a way that interactions occur only between nearest-neighbours. This structure is realized starting from a k-regular ring and by inserting, in the average, c additional links in such a way that k and c are tuneable parameters for the population architecture. We prove that this system exhibits a transition between regimes of localization (where the final number of stiflers is at most logarithmic in the population size) and propagation (where the final number of stiflers grows algebraically with the population size) at a finite value of the network parameter c. A quantitative estimate for the critical value of c is obtained via extensive numerical simulations. (AU)

FAPESP's process: 16/11648-0 - Limit theorems and phase transition results for information propagation models on graphs
Grantee:Pablo Martin Rodriguez
Support Opportunities: Regular Research Grants
FAPESP's process: 15/03868-7 - Asymptotic behavior of stochastic processes on graphs and applications
Grantee:Pablo Martin Rodriguez
Support Opportunities: Scholarships abroad - Research