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:
-
- School of Physics and Astronomy, University of Manchester, Manchester, M13 9Pl (United Kingdom)
- 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
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- 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); Journal ID: ISSN 0031-9007
- 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. https://doi.org/10.1103/PHYSREVLETT.98.150201
Bray, Alan J, and Dean, David S. 2007.
"Statistics of Critical Points of Gaussian Fields on Large-Dimensional Spaces". United States. https://doi.org/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},
url = {https://www.osti.gov/biblio/20951222},
journal = {Physical Review Letters},
issn = {0031-9007},
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}
}
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