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In magnetic recording, ac erased noise is the noise read back from a demagnetized medium and results from the discrete nature of the medium and the random polarization of the magnetic particles. Due to magnetic dipole interactions, the polarization of the particles is not entirely random. The nature of the correlation is studied using both experimental data and theoretical analysis. The approach is to derive the magnetization of an uncorrelated ensemble of magnetic particles of uniform density as a three-dimensional stationary Gaussian process. The effect of introducing correlation to the process is explored. Correlation along the record direction is shown to act as a low-pass filter. Correlation along the medium thickness results in a modified thickness loss term, and that across the track is shown to lead away from the usual linear dependence on the track width towards a quadratic dependence. The parameters specifying the assumed functional form for the filter function are determined using experimental data. Long-range correlation indicated by the data is shown to reduce the magnetic energy of the ensemble, and the functional form of the energy density is derived.