O. Alves, E. Lebensztayn, F. Machado, and M. Martinez, Random walks systems on complete graphs, Bulletin of the Brazilian Mathematical Society, New Series, vol.37, issue.4, pp.571-580, 2006.
DOI : 10.1007/s00574-006-0028-8

O. Alves, F. Machado, and S. Popov, Phase Transition for the Frog Model, Electronic Journal of Probability, vol.7, issue.0, p.pp, 2002.
DOI : 10.1214/EJP.v7-115

O. Alves, F. Machado, and S. Popov, The shape theorem for the frog model, The Annals of Applied Probability, vol.12, issue.2, pp.533-546, 2002.
DOI : 10.1214/aoap/1026915614

F. Baccelli, B. Blaszczyszyn, and M. Mirsadeghi, Optimal paths on the space-time SINR random graph, Advances in Applied Probability, vol.23, issue.01, pp.131-150, 2011.
DOI : 10.1214/aop/1176996798

URL : https://hal.archives-ouvertes.fr/inria-00433825

L. Baum and P. Billingsley, Asymptotic Distributions for the Coupon Collector's Problem, The Annals of Mathematical Statistics, vol.36, issue.6, pp.1835-1839, 1965.
DOI : 10.1214/aoms/1177699813

P. Billingsley, Convergence of probability measures, 1968.
DOI : 10.1002/9780470316962

S. Boucheron, F. Gamboa, and C. Léonard, Bins and balls; Large deviations of the empirical occupancy process, The Annals of Applied Probability, vol.12, issue.2, pp.607-636, 2002.
DOI : 10.1214/aoap/1026915618

F. Comets, J. Quastel, and A. , Fluctuations of the front in a stochastic combustion model, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.43, issue.2, pp.147-162, 2007.
DOI : 10.1016/j.anihpb.2006.01.005

URL : https://hal.archives-ouvertes.fr/hal-00013422

F. Comets, J. Quastel, and A. , Ramírez: Fluctuations of the front in a one dimensional model of X + Y ? 2X, Trans. Amer. Math. Soc, pp.361-6165, 2009.

D. Dacunha-castelle and M. Duflo, 2: temps mobile, Probabilités et Statistiques, 1983.

A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, 1998.

L. Ding and Z. , Modeling wireless sensor networks using random graph theory, Physica A: Statistical Mechanics and its Applications, vol.387, issue.12, pp.3008-3016, 2008.
DOI : 10.1016/j.physa.2008.01.029

P. Dupuis, C. Nuzman, and P. , Whiting: Large deviation asymptotics for occupancy problems, Ann. Probab, vol.32, pp.2765-2818, 2004.

T. Duquesne and J. Gall, Random trees, Lévy processes and spatial branching processes, 2002.

P. Erdös and A. , Rényi: On a classical problem of probability theory, Magyar Tud. Akad. Mat. Kutató Int. Közl, vol.6, pp.215-220, 1961.

J. Jacod and A. N. , Shiryaev: Limit theorems for stochastic processes, 2002.

X. Jia, Wireless networks and random geometric graphs, Proceedings of ISPAN'04 Algorithms and Networks), pp.575-580, 2004.

H. Kawahigashi, Y. Terashima, N. Miyauchi, and T. , Nakakawaji: Modeling ad-hoc sensor networks using random graph theory, Consumer Communications and Networking Conference, 2005. CCNC. 2005 Second IEEE

N. Kan, Martingale approach to the coupon collection problem, Journal of Mathematical Sciences, vol.22, issue.4, pp.113-126, 2002.
DOI : 10.1007/s10958-005-0134-y

H. Kesten and B. P. , A Limit Theorem for Multidimensional Galton-Watson Processes, The Annals of Mathematical Statistics, vol.37, issue.5, pp.1211-1223, 1966.
DOI : 10.1214/aoms/1177699266

H. Kesten and V. , The spread of a rumor or infection in a moving population, The Annals of Probability, vol.33, issue.6, pp.2402-2462, 2005.
DOI : 10.1214/009117905000000413

H. Kesten and V. , Sidoravicius: A phase transition in a model for the spread of an infection, Illinois J. Math, vol.50, pp.547-634, 2006.

I. Kurkova, S. Popov, and M. , Vachkovshaia: On infection spreading and competition between independent random walks, Electron. J. Proba, vol.9, pp.11-12, 2004.

T. Kurtz, E. Lebensztayn, A. R. Leichsenring, and F. P. Machado, Limit theorems for an epidemic model on the complete graph, ALEA Lat. Am. J. Probab. Math. Stat, vol.4, pp.45-55, 2008.

F. Machado, H. Machurian, and H. , Matzinger: CLT for the proportion of infected individuals for an epidemic model on a complete graph, Markov Proc. Related Fields, pp.209-224, 2011.

J. Neveu, Arbres et processus de Galton-Watson, Annales de l'IHP, Section B, vol.22, issue.2, pp.199-207, 1986.

J. Pitman, Combinatorial stochastic processes, Lect. Notes Math, vol.1875, 2002.

A. Ramírez and V. Sidoravicius, Asymptotic behavior of a stochastic combustion growth process, Journal of the European Mathematical Society, vol.6, pp.293-334, 2004.
DOI : 10.4171/JEMS/11

M. E. Zhukovski¨?zhukovski¨?, The law of large numbers for an epidemic model. (Russian) Dokl, Akad. Nauk Dokl. Math, vol.442, issue.85, pp.736-739, 2012.