Our goal is to study the 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 H-#lambda#W, with W being a positive definite matrix and H a random real symmetric one. We first consider spectra of the matrix pencils with independent, identically distributed entries of H. Then we concentrate on an infinite-range ('full-connectivity') version of a 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 the Wigner-Dyson theory of usual random matrices.
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