title: 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 landscape scenarios coming from the anthropic approach to string theory.
authors.affiliation: School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom.
authors.forename: Alan J
authors.initials: AJ
authors.lastname: Bray
authors.forename: David S
authors.initials: DS
authors.lastname: Dean