We consider a 2D electron system in a strong magnetic field, where the local Hall resistivity ρxy(r) is a function of position and ρₓₓ(r) is small compared to ρxy. Particularly if the correlations fall off slowly with distance, or if fluctuations exist on several length scales, one finds that the macroscopic longitudinal resistivity Rₓₓ is only weakly dependent on ρₓₓ and is approximately proportional to the magnitude of fluctuations in ρxy. This may provide an explanation of the empirical law Rₓₓ∝BdRxydB where Rxy is the Hall resistance, and B is the magnetic field.
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Simon et al. (1994) studied this question.
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