# 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

- 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}

}

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