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

Alan J. Bray·David S. Dean
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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.

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Alan J. Bray, David S. Dean. 2006-11-01. The statistics of critical points of Gaussian fields on large-dimensional spaces. https://doi.org/10.1103/physrevlett.98.150201

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