We consider transport in the Poissonian regime between edge states in the
quantum Hall effect. The backscattering potential is assumed to be arbitrary,
as it allows for multiple tunneling paths. We show that the Schottky relation
between the backscattering current and noise can be established in full
generality: the Fano factor corresponds to the electron charge (the
quasiparticle charge) in the integer (fractional) quantum Hall effect, as in
the case of purely local tunneling. We derive an analytical expression for the
backscattering current, which can be written as that of a local tunneling
current, albeit with a renormalized tunneling amplitude which depends on the
voltage bias. We apply our results to a separable tunneling amplitude which can
represent an extended point contact in the integer or in the fractional quantum
Hall effect. We show that the differential conductance of an extended quantum
point contact is suppressed by the interference between tunneling paths, and it
has an anomalous dependence with respect to the bias voltage
