  We derive the distribution of particle currents for a system of interacting
active Brownian particles in the long time limit using large deviation theory
and a weighted many body expansion. We find the distribution is non-Gaussian,
except in the limit of passive particles. The non-Gaussian fluctuations can be
understood from the effective potential the particles experience when
conditioned on a given current. This potential suppresses fluctuations of the
particles orientations and surrounding density, aligning particles and reducing
their effective drag. From the distribution of currents, we compute the
diffusion coefficient, which is in excellent agreement with molecular dynamics
simulations over a range of self-propulsion velocities and densities. We show
that mass transport is Fickian in that the diffusion constant determines the
response of a small density gradient, and that nonlinear responses are
similarly computable from the density dependence of the current distribution.
