The statistics of critical points of Gaussian fields on large-dimensional spaces

Abstract

We calculate the average number of critical points of a Gaussian field on a high-dimensional space as a function of their energy and their index. Our results give a complete picture of the organization of critical points and are of relevance to glassy and disordered systems, and to landscape scenarios coming from the anthropic approach to string theory.

5 pages

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• Large Deviations of Extreme Eigenvalues of Random Matrices
• Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids
• Cosmology From Random Multifield Potentials
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