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

Autor(es)

Agliari, Elena ^[1] ; Pachon, Angelica ^[2] ; Rodriguez, Pablo M. ^[3] ; Tavani, Flavia ^[1]

Afiliação do(s) autor(es)

^[1] Sapienza Univ Roma, Rome - Italy

^[2] Univ Turin, Turin - Italy

^[3] Univ Sao Paulo, Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 169, n. 4, p. 846-875, NOV 2017.
• Citações Web of Science: 2

Resumo

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)

• Processo FAPESP: 16/11648-0 - Teoremas limite e resultados de transição de fase para modelos de propagação de informação em grafos
• Beneficiário: Pablo Martin Rodriguez
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 15/03868-7 - Comportamento assintótico de processos estocásticos em grafos e aplicações
• Beneficiário: Pablo Martin Rodriguez
• Modalidade de apoio: Bolsas no Exterior - Pesquisa