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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. Onerealization of such a conductance is the Landauer transmission for manytransverse channels. On the other hand, the statistics of the one-channelLandauer transmission between two local probes is described by a multifractalspectrum that can be related to the singularity spectrum of individualeigenstates. To better understand the relations between these two types ofresults, we consider various scattering geometries that interpolate betweenthese 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 isolatedincoming wire and many outgoing wires, the transmission has the samemultifractal statistics as the local density of states of the site where theincoming wire arrives; (ii) in the presence of backward scattering channelswith respect to the case (i), the statistics of the transmission is notmultifractal anymore, but becomes monofractal. Finally, we also describe howthese scattering geometries influence the statistics of the transmission offcriticality.

Anderson transitions : multifractal or non-multifractal statistics of the transmission as a function of the scattering geometry