Within the Gaussian phantom-chain model of a polymer network, we demonstrate and apply the formal analogy between the problem of computing the force constants acting on a set of rigid filler particles and that of computing the capacity of a system of conductors in a dielectric medium. We find that a single spherical particle undergoes a mean-square displacement [(Delta X)(2)] from its equilibrium position which is inversely proportional to its radius R. It is thus subject to an isotropic harmonic potential with force constant [3k(B)T/[(Delta X)(2)]] proportional to R. Quantitative evaluation of the proportionality constant for typical unswollen networks shows that root[(Delta X)(2)]/R decreases from 10(-1) to 10(-5) as R increases from 10 nm to 1 mu m. The time scale of these fluctuations is independent of R and falls in the range 10(-4)-10(1) s. The fluctuations of two neighboring particles are not additive. A distance-dependent ＇＇stiffening＇＇ of the network is demonstrated through the calculation of the appropriate response and force constant matrices.