Artículos de revistas
Rumor Processes On ℕ And Discrete Renewal Processes
Registro en:
Journal Of Statistical Physics. Springer New York Llc, v. 155, n. 3, p. 591 - 602, 2014.
224715
10.1007/s10955-014-0959-1
2-s2.0-84898549254
Autor
Gallo S.
Garcia N.L.
Junior V.V.
Rodriguez P.M.
Institución
Resumen
We study two rumor processes on ℕ, the dynamics of which are related to an SI epidemic model with long range transmission. Both models start with one spreader at site 0 and ignorants at all the other sites of ℕ, 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 ℕ can be related to a suitably chosen discrete renewal process. © 2014 Springer Science+Business Media New York. 155 3 591 602 Andersson, H., Limit theorems for a random graph epidemic model (1998) Ann. Appl. Probab., 8 (4), pp. 1331-1349 Athreya, S., Roy, R., Sarkar, A., On the coverage of space by random sets (2004) Adv. Appl. Probab., 36 (1), pp. 1-18 Berger, N., Borgs, C., Chayes, J.T., Saberi, A., On the spread of viruses on the internet (2005) Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, , SODA '05 Bertacchi, D., Zucca, F., Rumor processes in random environment on ℕ and galton-watson trees (2013) J. Stat. Phys., 153 (3), pp. 486-511 Bressaud, X., Fernández, R., Galves, A., Decay of correlations for non-Hölderian dynamics. A coupling approach (1999) Elect. J. Probab, 4 (3), pp. 1-19 Coletti, C.F., Rodríguez, P.M., Schinazi, R.B., A spatial stochastic model for rumor transmission (2012) J. Stat. Phys., 147 (2), pp. 375-381 Comets, F., Delarue, D., Schott, R., Information transmission under random emission constraints Comb. Probab. Comput, , arXiv: 1309. 0624 (2013, to appear) Comets, F., Fernandez, R., Ferrari, P., Processes with long memory: regenerative construction and perfect simulation (2002) Ann. Appl. Prob., 12 (3), pp. 921-943 Daley, D.J., Kendall, D.G., Stochastic rumours (1965) J. Inst. Math. Appl., 1, pp. 42-55 Durrett, R., Jung, P., Two phase transitions for the contact process on small worlds (2007) Stoch. Process. Appl., 117 (12), pp. 1910-1927 Gallo, S., Lerasle, M., Takahashi, Y.D., Markov approximation of chains of infinite order in the d-metric (2013) Markov Process. Relat. Fields, 19 (1), pp. 51-82 Garsia, A., Lamperti, J., A discrete renewal theorem with infinite mean (1962) Comment. Math. Helv., 37, pp. 221-234 Isham, V., Harden, S., Nekovee, M., Stochastic epidemics and rumours on finite random networks (2010) Phys. A: Stat. Mech. Appl., 389 (3), pp. 561-576 Junior, V.V., Machado, F.P., Zuluaga, M., Rumor processes on ℕ (2011) J. Appl. Probab., 48 (3), pp. 624-636 Kurtz, T.G., Lebensztayn, E., Leichsenring, A.R., Machado, F.P., Limit theorems for an epidemic model on the complete graph. ALEA Lat (2008) Am. J. Probab. Math. Stat., 4, pp. 45-55 Lebensztayn, E., Machado, F.P., Rodríguez, P.M., Limit theorems for a general stochastic rumour model (2011) SIAM J. Appl. Math, 71 (4), pp. 1476-1486 Lebensztayn, E., Machado, F.P., Rodríguez, P.M., Process with random stifling (2011) Environ. Modell. Softw, 26 (4), pp. 517-522 Maki, D.P., Thompson, M., (1973) Mathematical Models and Applications: With Emphasis on the Social, Life, and Management Sciences, , Englewood Cliffs: Prentice-Hall Inc Moreno, Y., Nekovee, M., Pacheco, A.F., Dynamics of rumor spreading in complex networks (2004) Phys. Rev. E, 69, p. 066130 Pittel, B., On spreading a rumor (1987) SIAM J. Appl. Math., 47 (1), pp. 213-223 Ross, S.M., (2009) Introduction to Probability Models, , 10th edn., Burlington: Academic Press Inc