On the chemical distance for supercritical Bernoulli percolation, The Annals of Probability, vol.24, issue.2, pp.1036-1048, 1996. ,
DOI : 10.1214/aop/1039639377
On the mixing time of a simple random walk on the super critical percolation cluster. Probability theory and related fields, pp.408-420, 2003. ,
Anomalous heat-kernel decay for random walk among bounded random conductances. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, pp.374-392, 2008. ,
Isoperimetry in two-dimensional percolation. arXiv preprint, 2012. ,
The Wulff crystal in Ising and percolation models, volume 1878 of Lecture Notes in Mathematics Lectures from the 34th Summer School on Probability Theory held in Saint-Flour, 2004. ,
Weak shape theorem for first passage percolation with infinite passage times. Available from arxiv.org/abs, 1404. ,
Surface order large deviations for 2D FKpercolation and Potts models. Stochastic Process, Appl, vol.113, issue.1, pp.81-99, 2004. ,
The time constant of first-passage percolation on the square lattice, Advances in Applied Probability, vol.17, issue.04, pp.864-879, 1980. ,
DOI : 10.2307/1426744
Some limit theorems for percolation processes with necessary and sufficient conditions, Ann. Probab, vol.9, issue.4, pp.583-603, 1981. ,
On the continuity of the time constant of first-passage percolation, J. Appl. Probab, vol.18, issue.4, pp.809-819, 1981. ,
First Passage Percolation for Random Colorings of $\mathbb{Z}^d$, The Annals of Applied Probability, vol.3, issue.3, pp.746-762, 1993. ,
DOI : 10.1214/aoap/1177005361
Asymptotic shape for the chemical distance and first-passage percolation on the infinite Bernoulli cluster, ESAIM: Probability and Statistics, vol.8, pp.169-199, 2004. ,
DOI : 10.1051/ps:2004009
Large deviations for the chemical distance in supercritical Bernoulli percolation, The Annals of Probability, vol.35, issue.3, pp.833-866, 2007. ,
DOI : 10.1214/009117906000000881
URL : https://hal.archives-ouvertes.fr/hal-00002875
Moderate deviations for the chemical distance in Bernoulli percolation, ALEA Lat. Am. J. Probab. Math. Stat, vol.7, pp.171-191, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00401689
First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory, Proc. Internat, pp.61-110, 1965. ,
Aspects of first passage percolation, Lecture Notes in Math, vol.1180, pp.125-264, 1986. ,
DOI : 10.1007/BFb0074919
Percolation theory for mathematicians, of Progress in Probability and Statistics. Birkhäuser, 1982. ,
DOI : 10.1007/978-1-4899-2730-9
Aspects of first passage percolation, Lecture Notes in Math, vol.1180, pp.125-264, 1986. ,
DOI : 10.1007/BFb0074919
Domination by product measures, The Annals of Probability, vol.25, issue.1, pp.71-95, 1997. ,
DOI : 10.1214/aop/1024404279
Isoperimetry and heat kernel decay on percolation clusters. The Annals of Probability, pp.100-128, 2004. ,
A note on percolation on $Z^d$: isoperimetric profile via exponential cluster repulsion, Electronic Communications in Probability, vol.13, issue.0, pp.377-392, 2008. ,
DOI : 10.1214/ECP.v13-1390
Surface order large deviations for Ising, Potts and percolation models. Probab. Theory Related Fields, pp.427-466, 1996. ,
Concentration estimates for the isoperimetric constant of the super critical percolation cluster. Arxiv preprint arXiv:1110, 2011. ,
zur frage der geschwindigkeit des wachsthums und der auflösung der krystallflächen, Zeitschrift für Kristallographie-Crystalline Materials, vol.34, issue.1, pp.449-530, 1901. ,
Vandoeuvre-lès-Nancy, F-54506, France, E-mail address: Olivier.Garet@univ-lorraine.fr Université de Lorraine, Institut Élie Cartan de Lorraine-mail address: Regine.Marchand@univ-lorraine, pp.75205-75218 ,