  We study distribution functions (DF) of mesoscopic hopping conductance
numerically by searching for the shortest path. We have found that the
distributions obtained by choosing randomly the chemical potentials (for a
fixed impurity configuration), which corresponds to a typical experimental
situation, coincide with those obtained when both impurity configuration and
chemical potential is chosen randomly, in agreement with the ergodicity
hypothesis. The DFs obtained for one-dimensional systems were found to be quite
close to the independent predictions of V.I. Mel'nikov, A.A. Abrikosov and P.
Lee et al. For D=2, the DFs both for narrow system and thin film look similar
(and close to the 1D case).The distribution function for the conductance of the
square sample is nearly Gaussian as predicted by both Altshuler et al and
Serota et al.
