  We propose that "standard pings", brief broadband radio impulses, can be used
to study the three-dimensional clustering of matter in the Universe even in the
absence of redshift information. The dispersion of radio waves as they travel
through the intervening plasma can, like redshift, be used as a cosmological
distance measure. Because of inhomogeneities in the electron density along the
line of sight, dispersion is an imperfect proxy for radial distance and we show
that this leads to calculable dispersion-space distortions in the apparent
clustering of sources. Fast radio bursts (FRBs) are a new class of radio
transients that are the prototypical standard ping and, due to their high
observed dispersion, have been interpreted as originating at cosmological
distances. The rate of fast radio bursts has been estimated to be several
thousand over the whole sky per day and, if cosmological, the sources of these
events should trace the large-scale structure of the Universe. We calculate the
dispersion-space power spectra for a simple model where electrons and FRBs are
biased tracers of the large-scale structure of the Universe and we show that
the clustering signal could be measured using as few as 10 000 events. Such a
survey is in line with what may be achieved with upcoming wide-field radio
telescopes.
