  We consider the simple random walk on Z^d evolving in a potential of
independent and identically distributed random variables taking values in [0, +
\infty]. We give optimal conditions for the existence of the quenched
point-to-point Lyapunov exponent, and for different versions of a shape
theorem. The method of proof applies as well to first-passage percolation, and
builds up on an approach of Cox and Durrett (1981). The weakest form of shape
theorem holds whenever the set of sites with finite potential percolates. Under
this condition, we then show the existence of the quenched point-to-hyperplane
Lyapunov exponent, and give a large deviation principle for the walk under the
quenched weighted measure.
