  We consider fluctuations in the distribution of critical points - saddle
points, minima and maxima - of random gaussian fields. We calculate the
asymptotic limits of the two point correlation function for various critical
point densities, for both long and short range. We perform the calculation for
any dimension of the field, provide explicit formulae for two and three
dimensions, and verify our results with numerical calculations.

Disordered Systems and Neural Networks;Chaotic Dynamics;Data Analysis, Statistics and Probability