Statistics of Critical Points of Gaussian Fields on Large-Dimensional Spaces
Authors:
- 10 April 2007
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 98 (15) , 150201
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.Keywords
All Related Versions
This publication has 24 references indexed in Scilit:
- Complexity of Random Energy Landscapes, Glass Transition, and Absolute Value of the Spectral Determinant of Random MatricesPhysical Review Letters, 2004
- Stationary points and dynamics in high-dimensional systemsThe Journal of Chemical Physics, 2003
- Saddle points and dynamics of Lennard-Jones clusters, solids, and supercooled liquidsThe Journal of Chemical Physics, 2002
- Geometric Approach to the Dynamic Glass TransitionPhysical Review Letters, 2002
- Fragile vs . strong liquids: A saddles-ruled scenarioEurophysics Letters, 2001
- Stationary points of the Thouless-Anderson-Palmer free energyPhysical Review B, 1998
- Large time nonequilibrium dynamics of a particle in a random potentialPhysical Review E, 1996
- Dynamics of manifolds in random media: the selfconsistent Hartree approximationJournal de Physique I, 1993
- Replica field theory for random manifoldsJournal de Physique I, 1991
- On the statistical distribution of the widths and spacings of nuclear resonance levelsMathematical Proceedings of the Cambridge Philosophical Society, 1951