Counting Stationary Points of Random Landscapes as a Random Matrix Problem
| dc.creator | Fyodorov, Yan V | |
| dc.date | 2005-07-03 | |
| dc.date.accessioned | 2026-07-07T06:19:16Z | |
| dc.date.available | 2026-07-07T06:19:16Z | |
| dc.description | Finding the mean of the total number of stationary points for N-dimensional random Gaussian landscapes can be reduced to averaging the absolute value of characteristic polynomial of the corresponding Hessian. First such a reduction is illustrated for a class of models describing energy landscapes of elastic manifolds in random environment, and a general method of attacking the problem analytically is suggested. Then the exact solution to the problem [Phys. Rev. Lett. v.92 (2004) 240601] for a class of landscapes corresponding to the simplest, yet nontrivial "toy model" with N degrees of freedom is described. Asymptotic analysis reveals a phase transition to a glass-like state of the matter. | |
| dc.description | Presentation at "Applications of Random Matrices to Economy and Other Complex Systems", May 26-28, 2005, Krakow | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0507059 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0507059 | |
| dc.identifier | Acta Physica Polonica B, v.36 (2005), 2699-2707 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95013 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Counting Stationary Points of Random Landscapes as a Random Matrix Problem | |
| dc.type | text |