  We propose exact results for the full counting statistics, or the scaled
cumulant generating function, pertaining to the transfer of arbitrary conserved
quantities across an interface in homogeneous integrable models out of
equilibrium. We do this by combining insights from generalised hydrodynamics
with a theory of large deviations in ballistic transport. The results are
applicable to a wide variety of physical systems, including the Lieb-Liniger
gas and the Heisenberg chain. We confirm the predictions in non-equilibrium
steady states obtained by the partitioning protocol, by comparing with Monte
Carlo simulations of this protocol in the classical hard rod gas. We verify
numerically that the exact results obey the correct non-equilibrium fluctuation
relations with the appropriate initial conditions.
