  We study, on a $d$ dimensional hypercubic lattice, a random walk which is
homogeneous except for one site. Instead of visiting this site, the walker hops
over it with arbitrary rates. The probability distribution of this walk and the
statistics associated with the hop-overs are found exactly. This analysis
provides a simple approach to the problem of tagged diffusion, i.e., the
movements of a tracer particle due to the diffusion of a vacancy. Applications
to vacancy mediated disordering are given through two examples.
