  We present and solve a continuum theory of vacancy-mediated diffusion (as
evidenced, for example, in the vacancy driven motion of tracers in crystals).
Results are obtained for all spatial dimensions, and reveal the strongly
non-gaussian nature of the tracer fluctuations. In integer dimensions, our
results are in complete agreement with those from previous exact lattice
calculations. We also extend our model to describe the vacancy-driven
fluctuations of a slaved flux line.
