First-passage percolation is a time-dependent generalization of discrete Bernoulli percolation in which each graph edge e of Z^d is assigned a nonnegative random variable t = t(e) called a time coordinate, the collection of which are identically and independently distributed . Within this model, the main objects of study are the asymptotic properties as t->∞ of the set B^~(t) = {v element Z^d :T(0, v)<=t} where T(u, v) = inf{T(r):r is a path from u to v} is the so-called travel time from u to v and where T(r) = sum_(i = 1)^n t(e_i)

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