Random walk on the incipient infinite cluster for oriented percolation

We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation in d spatial dimensions and one time dimension. For 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.