Full counting statistics for noninteracting fermions: Joint probability distributions

The joint probability distribution in the full counting statistics (FCS) for noninteracting electrons is discussed for an arbitrary number of initially separate subsystems which are connected at t=0 and separated at a later time. A simple method to obtain the leading order long time contribution to the logarithm of the characteristic function is presented which simplifies earlier approaches. New explicit results for the determinant involving the scattering matrices are found. The joint probability distribution for two leads is discussed for Y-junctions and dots connected to four leads.