  Chiral edge modes of topological insulators and Hall states exhibit
non-trivial behavior of conductance in the presence of impurities or additional
channels. We will present a simple formula for the conductance through a chiral
edge mode coupled to a disordered bulk. For a given coupling matrix between the
chiral mode and bulk modes, and a Green function matrix of bulk modes in real
space, the renormalized Green function of the chiral mode is expressed in
closed form as a ratio of determinants. We demonstrate the usage of the formula
in two systems: i) a 1d wire with random onsite impurity potentials for which
we found the disorder averaging is made simpler with the formula, and ii) a
quantum Hall fluid with impurities in the bulk for which the phase picked up by
the chiral mode due to the scattering with the impurities can be conveniently
estimated.
