Critical point correlations in random gaussian fields

Abstract

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.

19 pages, 3 figures, accepted to J.Phys.A

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Cited by in corpus (3)

• Critical Behaviour of the Number of Minima of a Random Landscape at the Glass Transition Point and the Tracy-Widom distribution
• Nodal portraits of quantum billiards: Domains, lines, and statistics
• Energy Landscape of the Finite-Size Mean-field 2-Spin Spherical Model and Topology Trivialization