The aim of this paper is to generalize the well-known asymptotic shape result
for first-passage percolation on \Zd to first-passage percolation on a random
environment given by the infinite cluster of a supercritical Bernoulli
percolation model. We prove the convergence of the renormalized set of wet
points to a deterministic shape that does not depend on the random environment.
As a special case of the previous result, we obtain an asymptotic shape theorem
for the chemical distance in supercritical Bernoulli percolation. We also prove
a flat edge result. Some various examples are also given.Comment: redaction du 10 avril 200
