K. S. Alexander, Approximation of subadditive functions and convergence rates in limiting-shape results, The Annals of Probability, vol.25, issue.1, pp.30-55, 1997.
DOI : 10.1214/aop/1024404277

M. Deijfen, O. Häggström, and J. Bagley, A stochastic model for competing growth on R d . Markov Process, pp.217-248, 2004.

M. Deijfen and O. Häggström, Nonmonotonic Coexistence Regions for the Two-Type Richardson Model on Graphs, Electronic Journal of Probability, vol.11, issue.0, 2006.
DOI : 10.1214/EJP.v11-321

O. Garet and R. Marchand, Coexistence in two-type first-passage percolation models, The Annals of Applied Probability, vol.15, issue.1A, pp.298-330, 2005.
DOI : 10.1214/105051604000000503

URL : https://hal.archives-ouvertes.fr/hal-00000971

O. Garet and R. Marchand, Large deviations for the chemical distance in supercritical Bernoulli percolation, The Annals of Probability, vol.35, issue.3
DOI : 10.1214/009117906000000881

URL : https://hal.archives-ouvertes.fr/hal-00002875

O. Garet and R. Marchand, Competition between growths governed by Bernoulli percolation. Markov Process. Related Fields, to appear
URL : https://hal.archives-ouvertes.fr/hal-00005783

J. Gouéré, Shape of territories in some competing growth models. Preprint, available at http://arxiv.org/abs/math, 2006.

G. Grimmett and H. Kesten, First-passage percolation, network flows and electrical resistances, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.15, issue.3, pp.335-366, 1984.
DOI : 10.1007/BF00533701

O. Häggström and R. Pemantle, First passage percolation and a model for competing spatial growth, Journal of Applied Probability, vol.35, issue.03, pp.683-692, 1998.
DOI : 10.1017/S0305004100077288

O. Häggström and R. Pemantle, Absence of mutual unbounded growth for almost all parameter values in the two-type Richardson model, Stochastic Processes and their Applications, vol.90, issue.2, pp.207-222, 2000.
DOI : 10.1016/S0304-4149(00)00042-9

C. Hoffman, Coexistence for Richardson type competing spatial growth models, The Annals of Applied Probability, vol.15, issue.1B, pp.739-747, 2005.
DOI : 10.1214/105051604000000729

C. Hoffman, Geodesics in first passage percolation. Preprint, available at http://arxiv.org/abs/math, 2005.

H. Kesten, On the Speed of Convergence in First-Passage Percolation, The Annals of Applied Probability, vol.3, issue.2, pp.296-338, 1993.
DOI : 10.1214/aoap/1177005426

J. Van-den, H. Berg, and . Kesten, Inequalities for the Time Constant in First-Passage Percolation, The Annals of Applied Probability, vol.3, issue.1, pp.56-80, 1993.
DOI : 10.1214/aoap/1177005507

B. P. Laboratoire-de-mathématiques, 6759, 45067 Orléans Cedex 2 France E-mail address: Olivier.Garet@univ-orleans.fr Institut Elie Cartan Nancy (mathématiques), Université Henri Poincaré Nancy 1, Campus Scientifique