  We present accurate predictions of the correlation function of hotspots in
the microwave background radiation for gaussian theories such as those
predicted in most inflation models. The correlation function of peaks above a
certain threshold depends only on the threshold and the power spectrum of
temperature fluctuations. Since there are both potentially observable
quantities in a microwave background map, there are no adjustable parameters in
the predictions. These correlations should therefore provide a powerful test of
the gaussian hypothesis, and provide a useful discriminant between inflation
and topological defect models such as the cosmic string model. The correlations
have a number of oscillatory features, which should be detectable at high
signal-to-noise with future satellite experiments such as MAP and Planck.
