  We have used modern supercomputer facilities to carry out extensive numerical
simulations of statistical properties of 1D and 2D arrays of single-electron
islands with random background charges, in the limit of small island
self-capacitance. In particular, the spectrum of single-electron addition
energies shows a clear Coulomb gap that, in 2D arrays, obeys the
Efros-Shklovskii theory modified for the specific electron-electron interaction
law. The Coulomb blockade threshold voltage statistics for 1D arrays is very
broad, with r.m.s. width $\delta V_t$ growing as $<V_t > \propto N^{1/2}$ with
the array size $N$. On the contrary, in square 2D arrays of large size the
distribution around $<V_t> \propto N$ becomes relatively narrow $(\delta V_t/<
V_t> \propto 1/N)$, and the dc $I$-$V$ curves are virtually universal. At low
voltages, the slope $G_0(T)$ of $I$-$V$ curves obeys the Arrhenius law. The
corresponding activation energy $U_0$ grows only slowly with $N$ and is
considerably lower than the formally calculated "lowest pass" energy $E_{max}$
of the potential profile, thus indicating the profile "softness".
