Invariant joint distribution of a stationary random field and its derivatives: Euler characteristic and critical point counts in 2 and 3D
Abstract
The full moments expansion of the joint probability distribution of an isotropic random field, its gradient, and invariants of the Hessian are presented in 2 and 3D. It allows for explicit expression for the Euler characteristic in ND and computation of extrema counts as functions of the excursion set threshold and the spectral parameter, as illustrated on model examples.
- Publication:
-
Physical Review D
- Pub Date:
- October 2009
- DOI:
- 10.1103/PhysRevD.80.081301
- arXiv:
- arXiv:0907.1437
- Bibcode:
- 2009PhRvD..80h1301P
- Keywords:
-
- 02.50.Sk;
- 02.50.Cw;
- 98.65.Dx;
- 98.80.Jk;
- Multivariate analysis;
- Probability theory;
- Superclusters;
- large-scale structure of the Universe;
- Mathematical and relativistic aspects of cosmology;
- Astrophysics - Cosmology and Nongalactic Astrophysics;
- Mathematical Physics;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 4 pages, 2 figures. Corrected expansion coefficients for orders n>