  We construct the equations of motion for the coupled dynamics of order
parameter and concentration for the nematic phase of driven particles on a
solid surface, and show that they imply (i) giant number fluctuations, with a
standard deviation proportional to the mean and (ii) long-time tails $\sim
t^{-d/2}$ in the autocorrelation of the particle velocities in $d$ dimensions
despite the absence of a hydrodynamic velocity field. Our predictions can be
tested in experiments on aggregates of amoeboid cells as well as on layers of
agitated granular matter.
