  Random inductor-capacitor (LC) networks can exhibit percolative
superconductor-insulator transitions (SITs). We use a simple and efficient
algorithm to compute the dynamical conductivity \sigma(\omega,p) of one type of
LC network on large (4000 x 4000) square lattices, where \delta=p-p_c is the
tuning parameter for the SIT. We confirm that the conductivity obeys a scaling
form, so that the characteristic frequency scales as \Omega ~ |\delta|^{\nu z}
with \nu z \approx 1.91, the superfluid stiffness scales as \Upsilon ~
|\delta|^t with t \approx 1.3, and the electric susceptibility scales as \chi_E
~ |\delta|^{-s} with s = 2\nu z - t \approx 2.52. In the insulating state, the
low-frequency dissipative conductivity is exponentially small, whereas in the
superconductor, it is linear in frequency. The sign of Im \sigma(\omega) at
small \omega changes across the SIT. Most importantly, we find that right at
the SIT Re \sigma(\omega) ~ \omega^{t/\nu z-1} ~ \omega^{-0.32}, so that the
conductivity diverges in the DC limit, in contrast with most other classical
and quantum models of SITs.
