  We investigate the three-dimensional clustering of sources emitting
electromagnetic pulses traveling through cold electron plasma, whose radial
distance is inferred from their dispersion measure. As a distance indicator,
dispersion measure is systematically affected by inhomogeneities in the
electron density along the line of sight and special and general relativistic
effects, similar to the case of redshift surveys. We present analytic
expressions for the correlation function of fast radio bursts (FRBs), and for
the galaxy-FRB cross-correlation function, in the presence of these dispersion
measure-space distortions. We find that the even multipoles of these
correlations are primarily dominated by non-local contributions (e.g. the
electron density fluctuations integrated along the line of sight), while the
dipole also receives a significant contribution from the Doppler effect, one of
the major relativistic effects. A large number of FRBs,
$\mathcal{O}(10^{5}\sim10^{6})$, expected to be observed in the Square
Kilometre Array, would be enough to measure the even multipoles at very high
significance, ${\rm S}/{\rm N} \approx 100$, and perhaps to make a first
detection of the dipole (${\rm S}/{\rm N} \approx 10$) in the FRB correlation
function and FRB-galaxy cross correlation function. This measurement could open
a new window to study and test cosmological models.
