  We consider simple random walk on the incipient infinite cluster for the
spread-out model of oriented percolation on $Z^d \times Z_+$. In dimensions
$d>6$, we obtain bounds on exit times, transition probabilities, and the range
of the random walk, which establish that the spectral dimension of the
incipient infinite cluster is 4/3, and thereby prove a version of the
Alexander--Orbach conjecture in this setting. The proof divides into two parts.
One part establishes general estimates for simple random walk on an arbitrary
infinite random graph, given suitable bounds on volume and effective resistance
for the random graph. A second part then provides these bounds on volume and
effective resistance for the incipient infinite cluster in dimensions $d>6$, by
extending results about critical oriented percolation obtained previously via
the lace expansion.
