Rumor Processes on and Discrete Renewal Processes

Autor(es)

Gallo, Sandro ^[1] ; Garcia, Nancy L. ^[2] ; Vargas Junior, Valdivino ^[3] ; Rodriguez, Pablo M. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Fed Rio de Janeiro, Inst Matemat, Dept Metodos Estat, Rio de Janeiro - Brazil

^[2] Univ Fed Rio de Janeiro, Inst Matemat Estat & Computacao Cientif, Dept Metodos Estat, Rio de Janeiro - Brazil

^[3] Univ Fed Goias, Inst Matemat & Estat, Goiania - Brazil

^[4] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, Dept Matemat Appl & Estat, Sao Carlos - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 155, n. 3, p. 591-602, MAY 2014.
• Citações Web of Science: 5

Resumo

We study two rumor processes on , the dynamics of which are related to an SI epidemic model with long range transmission. Both models start with one spreader at site and ignorants at all the other sites of , but differ by the transmission mechanism. In one model, the spreaders transmit the information within a random distance on their right, and in the other the ignorants take the information from a spreader within a random distance on their left. We obtain the probability of survival, information on the distribution of the range of the rumor and limit theorems for the proportion of spreaders. The key step of our proofs is to show that, in each model, the position of the spreaders on can be related to a suitably chosen discrete renewal process. (AU)

• Processo FAPESP: 13/03898-8 - Modelagem estocástica da difusão de uma informação em sistemas interagentes
• Beneficiário: Pablo Martin Rodriguez
• Modalidade de apoio: Auxílio à Pesquisa - Regular