Open Access
2008 On the birth-and-assassination process, with an application to scotching a rumor in a network
Charles Bordenave
Author Affiliations +
Electron. J. Probab. 13: 2014-2030 (2008). DOI: 10.1214/EJP.v13-573
Abstract

We give new formulas on the total number of born particles in the stable birth-and-assassination process, and prove that it has a heavy-tailed distribution. We also establish that this process is a scaling limit of a process of rumor scotching in a network, and is related to a predator-prey dynamics.

References

1.

Aldous, David. Asymptotics in the random assignment problem. Probab. Theory Related Fields 93 (1992), no. 4, 507–534. MR1183889 0767.60006 10.1007/BF01192719Aldous, David. Asymptotics in the random assignment problem. Probab. Theory Related Fields 93 (1992), no. 4, 507–534. MR1183889 0767.60006 10.1007/BF01192719

2.

Aldous, David; Krebs, William B. The “birth-and-assassination” process. Statist. Probab. Lett. 10 (1990), no. 5, 427–430. 0712.60090 10.1016/0167-7152(90)90024-2Aldous, David; Krebs, William B. The “birth-and-assassination” process. Statist. Probab. Lett. 10 (1990), no. 5, 427–430. 0712.60090 10.1016/0167-7152(90)90024-2

3.

Aldous, David; Steele, J. Michael. The objective method: probabilistic combinatorial optimization and local weak convergence. Probability on discrete structures, 1–72, Encyclopaedia Math. Sci., 110, Springer, Berlin, 2004. 1037.60008Aldous, David; Steele, J. Michael. The objective method: probabilistic combinatorial optimization and local weak convergence. Probability on discrete structures, 1–72, Encyclopaedia Math. Sci., 110, Springer, Berlin, 2004. 1037.60008

4.

Andersson, Håkan. Epidemic models and social networks. Math. Sci. 24 (1999), no. 2, 128–147.Andersson, Håkan. Epidemic models and social networks. Math. Sci. 24 (1999), no. 2, 128–147.

5.

Athreya, Krishna B.; Ney, Peter E. Branching processes. Die Grundlehren der mathematischen Wissenschaften, Band 196. Springer-Verlag, New York-Heidelberg, 1972. xi+287 pp. MR0373040Athreya, Krishna B.; Ney, Peter E. Branching processes. Die Grundlehren der mathematischen Wissenschaften, Band 196. Springer-Verlag, New York-Heidelberg, 1972. xi+287 pp. MR0373040

6.

Häggström, Olle; Pemantle, Robin. First passage percolation and a model for competing spatial growth. J. Appl. Probab. 35 (1998), no. 3, 683–692.Häggström, Olle; Pemantle, Robin. First passage percolation and a model for competing spatial growth. J. Appl. Probab. 35 (1998), no. 3, 683–692.

7.

Kordzakhia, George. The escape model on a homogeneous tree. Electron. Comm. Probab. 10 (2005), 113–124 (electronic). 1111.60075 10.1214/ECP.v10-1140Kordzakhia, George. The escape model on a homogeneous tree. Electron. Comm. Probab. 10 (2005), 113–124 (electronic). 1111.60075 10.1214/ECP.v10-1140

8.

Kordzakhia, George; Lalley, Steven P. A two-species competition model on $\Bbb Z\sp d$. Stochastic Process. Appl. 115 (2005), no. 5, 781–796. 1081.60068 10.1016/j.spa.2004.12.003Kordzakhia, George; Lalley, Steven P. A two-species competition model on $\Bbb Z\sp d$. Stochastic Process. Appl. 115 (2005), no. 5, 781–796. 1081.60068 10.1016/j.spa.2004.12.003

9.

Mitzenmacher, Michael. A brief history of generative models for power law and lognormal distributions. Internet Math. 1 (2004), no. 2, 226–251. MR2077227 1063.68526 10.1080/15427951.2004.10129088 euclid.im/1089229510Mitzenmacher, Michael. A brief history of generative models for power law and lognormal distributions. Internet Math. 1 (2004), no. 2, 226–251. MR2077227 1063.68526 10.1080/15427951.2004.10129088 euclid.im/1089229510

10.

The structure and dynamics of networks. Edited by Mark Newman, Albert-László Barabási and Duncan J. Watts. Princeton Studies in Complexity. Princeton University Press, Princeton, NJ, 2006. x+582 pp. ISBN: 978-0-691-11357-9; 0-691-11357-2The structure and dynamics of networks. Edited by Mark Newman, Albert-László Barabási and Duncan J. Watts. Princeton Studies in Complexity. Princeton University Press, Princeton, NJ, 2006. x+582 pp. ISBN: 978-0-691-11357-9; 0-691-11357-2

11.

Special issue on dynamic information dissemination. Edited by K. Ramaitham and P. E. Shenoy. IEEE Internet Computing, 2007. 11:14–44.Special issue on dynamic information dissemination. Edited by K. Ramaitham and P. E. Shenoy. IEEE Internet Computing, 2007. 11:14–44.

12.

Resnick, Sidney I. Heavy-tail phenomena. Probabilistic and statistical modeling. Springer Series in Operations Research and Financial Engineering. Springer, New York, 2007. xx+404 pp. ISBN: 978-0-387-24272-9; 0-387-24272-4 1152.62029Resnick, Sidney I. Heavy-tail phenomena. Probabilistic and statistical modeling. Springer Series in Operations Research and Financial Engineering. Springer, New York, 2007. xx+404 pp. ISBN: 978-0-387-24272-9; 0-387-24272-4 1152.62029

13.

Richardson, Daniel. Random growth in a tessellation. Proc. Cambridge Philos. Soc. 74 (1973), 515–528. 0295.62094 10.1017/S0305004100077288Richardson, Daniel. Random growth in a tessellation. Proc. Cambridge Philos. Soc. 74 (1973), 515–528. 0295.62094 10.1017/S0305004100077288

14.

Tsitsiklis, John N.; Papadimitriou, Christos H.; Humblet, Pierre. The performance of a precedence-based queueing discipline. J. Assoc. Comput. Mach. 33 (1986), no. 3, 593–602.Tsitsiklis, John N.; Papadimitriou, Christos H.; Humblet, Pierre. The performance of a precedence-based queueing discipline. J. Assoc. Comput. Mach. 33 (1986), no. 3, 593–602.
Charles Bordenave "On the birth-and-assassination process, with an application to scotching a rumor in a network," Electronic Journal of Probability 13(none), 2014-2030, (2008). https://doi.org/10.1214/EJP.v13-573
Accepted: 11 November 2008; Published: 2008
Vol.13 • 2008
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