  The scaling theory of Anderson localization is based on a global conductance
$g_L$ that remains a random variable of order O(1) at criticality. One
realization of such a conductance is the Landauer transmission for many
transverse channels. On the other hand, the statistics of the one-channel
Landauer transmission between two local probes is described by a multifractal
spectrum that can be related to the singularity spectrum of individual
eigenstates. To better understand the relations between these two types of
results, we consider various scattering geometries that interpolate between
these two cases and analyse the statistics of the corresponding transmissions.
We present detailed numerical results for the power-law random banded matrices
(PRBM model). Our conclusions are : (i) in the presence of one isolated
incoming wire and many outgoing wires, the transmission has the same
multifractal statistics as the local density of states of the site where the
incoming wire arrives; (ii) in the presence of backward scattering channels
with respect to the case (i), the statistics of the transmission is not
multifractal anymore, but becomes monofractal. Finally, we also describe how
these scattering geometries influence the statistics of the transmission off
criticality.
