The Average Transport Path Length in Scattering Media

For connected regions of arbitrary shape containing a distribution of scattering centers that need not be homogeneous, the average path length for particles that traverse the medium is shown to be unaffected by the presence of the scattering centers, provided that the incidence of the particles is uniform and isotropic, that no absorption or particle reproduction occurs in the medium, and that the scattering probabilities satisfy detailed balance.