First-passage percolation is a time-dependent generalization of discrete Bernoulli percolation in which each graph edge 
of 
is assigned a nonnegative random variable 
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 
of the set
 |
(1)
|
where
 |
(2)
|
is the so-called travel time from 
to 
and where
 |
(3)
|
is the so-called passage time of a path 
on 
which runs successively through the edges 
.
is interpreted as the collection of vertices which
can be reached from the origin by time 
.
Versions of the first-passage model based on site percolation, in which the 
's are assigned to vertices
rather than edges, have also been considered though
haven't been written about extensively (Kesten 1987).
