  We have extended our supercomputer-enabled Monte Carlo simulations of hopping
transport in completely disordered 2D conductors to the case of substantial
electron-electron Coulomb interaction. Such interaction may not only suppress
the average value of hopping current, but also affect its fluctuations rather
substantially. In particular, the spectral density $S_I (f)$ of current
fluctuations exhibits, at sufficiently low frequencies, a $1/f$-like increase
which approximately follows the Hooge scaling, even at vanishing temperature.
At higher $f$, there is a crossover to a broad range of frequencies in which
$S_I (f)$ is nearly constant, hence allowing characterization of the current
noise by the effective Fano factor $F\equiv S_I(f)/2e \left< I\right>$. For
sufficiently large conductor samples and low temperatures, the Fano factor is
suppressed below the Schottky value (F=1), scaling with the length $L$ of the
conductor as $F = (L_c / L)^{\alpha}$. The exponent $\alpha$ is significantly
affected by the Coulomb interaction effects, changing from $\alpha = 0.76 \pm
0.08$ when such effects are negligible to virtually unity when they are
substantial. The scaling parameter $L_c$, interpreted as the average
percolation cluster length along the electric field direction, scales as $L_c
\propto E^{-(0.98 \pm 0.08)}$ when Coulomb interaction effects are negligible
and $L_c \propto E^{-(1.26 \pm 0.15)}$ when such effects are substantial, in
good agreement with estimates based on the theory of directed percolation.
