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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:
 [1];  [2]
  1. School of Physics and Astronomy, University of Manchester, Manchester, M13 9Pl (United Kingdom)
  2. Laboratoire de Physique Theorique (UMR 5152 du CNRS), Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4 (France)
Publication Date:
OSTI Identifier:
20951222
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 15; Other Information: DOI: 10.1103/PhysRevLett.98.150201; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MANY-DIMENSIONAL CALCULATIONS; MATHEMATICAL SPACE; STATISTICS; STRING MODELS; STRING THEORY

Citation Formats

Bray, Alan J., and Dean, David S. Statistics of Critical Points of Gaussian Fields on Large-Dimensional Spaces. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.150201.
Bray, Alan J., & Dean, David S. Statistics of Critical Points of Gaussian Fields on Large-Dimensional Spaces. United States. doi:10.1103/PHYSREVLETT.98.150201.
Bray, Alan J., and Dean, David S. Fri . "Statistics of Critical Points of Gaussian Fields on Large-Dimensional Spaces". United States. doi:10.1103/PHYSREVLETT.98.150201.
@article{osti_20951222,
title = {Statistics of Critical Points of Gaussian Fields on Large-Dimensional Spaces},
author = {Bray, Alan J. and Dean, David S.},
abstractNote = {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.},
doi = {10.1103/PHYSREVLETT.98.150201},
journal = {Physical Review Letters},
number = 15,
volume = 98,
place = {United States},
year = {Fri Apr 13 00:00:00 EDT 2007},
month = {Fri Apr 13 00:00:00 EDT 2007}
}