  Our goal is to study statistical properies of "dielectric resonances" which
are poles of conductance of a large random $LC$ network. Such poles are a
particular example of eigenvalues $\lambda_n$ of matrix pencils ${\bf
H}-\lambda {\bf W}$, with ${\bf W}$ being positive definite matrix and ${\bf
H}$ a random real symmetric one. We first consider spectra of matrix pencils
with independent, identically distributed entries of ${\bf H}$. Then we
concentrate on an infinite-range ("full-connectivity") version of random $LC$
network. In all cases we calculate the mean eigenvalue density and the
two-point correlation function in the framework of Efetov's supersymmetry
approach. Fluctuations in spectra turn out to be the same as those provided by
Wigner-Dyson theory of usual random matrices.
