The distribution of extremal points of Gaussian scalar fields
| dc.creator | Foltin, Georg | |
| dc.date | 2003-01-29 | |
| dc.date | 2003-04-14 | |
| dc.date.accessioned | 2026-07-07T10:50:34Z | |
| dc.date.available | 2026-07-07T10:50:34Z | |
| dc.description | We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we compute the average density for a field in half-space with Dirichlet boundary conditions. Then we calculate the charge-charge correlation function (without boundary). We apply the general results to random waves and random surfaces. Furthermore, we find a generating functional for the two-point function. Its Legendre transform is the integral over the scalar curvature of a 4-dimensional Riemannian manifold. | |
| dc.description | 22 pages, 8 figures, corrected published version | |
| dc.identifier | https://arxiv.org/abs/math-ph/0301041 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0301041 | |
| dc.identifier | J.Phys.A36:4561-4580,2003 | |
| dc.identifier | doi:10.1088/0305-4470/36/16/307 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/184576 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Differential Geometry | |
| dc.subject | Chaotic Dynamics | |
| dc.title | The distribution of extremal points of Gaussian scalar fields | |
| dc.type | text |