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
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
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
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
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
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
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
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
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
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
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
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.