Conductance fluctuations in the localized regime

We have studied numerically the fluctuations of the conductance, $g$, in two-dimensional, three-dimensional and four-dimensional disordered non-interacting systems. We have checked that the variance of $\ln g$ varies with the lateral sample size as $L^{2\mathrm{/}5}$ in three-dimensional systems, and as a logarithm in four-dimensional systems. The precise knowledge of the dependence of this variance with system size allows us to test the single-parameter scaling hypothesis in three-dimensional systems. We have also calculated the third cumulant of the distribution of $\ln g$ in two- and three-dimensional systems, and have found that in both cases it diverges with the exponent of the variance times 3/2, remaining relevant in the large size limit.