References

• Addario-Berry, L.; Broutin, N. Total progeny in killed branching random walk. Probab. Theory Related Fields 151 (2011), no. 1-2, 265--295. MR2834719
• Aidekon, Elie. Tail asymptotics for the total progeny of the critical killed branching random walk. Electron. Commun. Probab. 15 (2010), 522--533. MR2737710
• Elie Aïdékon, Yueyun Hu, and Olivier Zindy. The precise tail behavior of the total progeny of a killed branching random walk. arXiv:1102.5536.
• Aldous, David; Krebs, William B. The "birth-and-assassination'' process. Statist. Probab. Lett. 10 (1990), no. 5, 427--430. MR1078244
• Andersson, Hakan. Epidemic models and social networks. Math. Sci. 24 (1999), no. 2, 128--147. MR1746332
• Athreya, Krishna B.; Ney, Peter E. Branching processes. Die Grundlehren der mathematischen Wissenschaften, Band 196. Springer-Verlag, New York-Heidelberg, 1972. xi+287 pp. MR0373040
• Berard, Jean; Gouere, Jean-Baptiste. Survival probability of the branching random walk killed below a linear boundary. Electron. J. Probab. 16 (2011), no. 14, 396--418. MR2774095
• Bordenave, Charles. On the birth-and-assassination process, with an application to scotching a rumor in a network. Electron. J. Probab. 13 (2008), no. 66, 2014--2030. MR2453554
• Brunet, Eric; Derrida, Bernard. Shift in the velocity of a front due to a cutoff. Phys. Rev. E (3) 56 (1997), no. 3, part A, 2597--2604. MR1473413
• Dembo, Amir; Zeitouni, Ofer. Large deviations techniques and applications. Corrected reprint of the second (1998) edition. Stochastic Modelling and Applied Probability, 38. Springer-Verlag, Berlin, 2010. xvi+396 pp. ISBN: 978-3-642-03310-0 MR2571413
• Gantert, Nina; Hu, Yueyun; Shi, Zhan. Asymptotics for the survival probability in a killed branching random walk. Ann. Inst. Henri Poincare Probab. Stat. 47 (2011), no. 1, 111--129. MR2779399
• Haggstrom, Olle; Pemantle, Robin. First passage percolation and a model for competing spatial growth. J. Appl. Probab. 35 (1998), no. 3, 683--692. MR1659548
• Hartman, Philip. Ordinary differential equations. John Wiley & Sons, Inc., New York-London-Sydney 1964 xiv+612 pp. MR0171038
• Heyde, C. C. Extension of a result of Seneta for the super-critical Galton-Watson process. Ann. Math. Statist. 41 1970 739--742. MR0254929
• Kordzakhia, George. The escape model on a homogeneous tree. Electron. Comm. Probab. 10 (2005), 113--124 (electronic). MR2150700
• Kordzakhia, George; Lalley, Steven P. A two-species competition model on $\Bbb Z^ d$. Stochastic Process. Appl. 115 (2005), no. 5, 781--796. MR2132598
• Igor Kortchemski. Predator-prey dynamics on infinite trees: a branching random walk approach. 1312.4933.
• Mueller, Carl; Mytnik, Leonid; Quastel, Jeremy. Effect of noise on front propagation in reaction-diffusion equations of KPP type. Invent. Math. 184 (2011), no. 2, 405--453. MR2793860
• The structure and dynamics of networks. Edited by Mark Newman, Albert-Laszlo Barabasi 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 MR2352222
• K. Ramamritham and P. Shenoy (Editors). Special issue on dynamic information dissemination. IEEE Internet Computing, 11:14--44, 2007.
• Richardson, Daniel. Random growth in a tessellation. Proc. Cambridge Philos. Soc. 74 (1973), 515--528. MR0329079
• Russell Lyons with Yuval Peres. Probability on Trees and Networks. In preparation. Available at http://mypage.iu.edu/~rdlyons/. Cambridge University Press, New York, 2007.
• Seneta, E. On recent theorems concerning the supercritical Galton-Watson process. Ann. Math. Statist. 39 1968 2098--2102. MR0234530
• 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. MR0849031