Probability Distribution of Curvatures of Isosurfaces in Gaussian Random Fields
arXiv:math-ph/0702031
Abstract
An expression for the joint probability distribution of the principal curvatures at an arbitrary point in the ensemble of isosurfaces defined on isotropic Gaussian random fields on Rn is derived. The result is obtained by deriving symmetry properties of the ensemble of second derivative matrices of isotropic Gaussian random fields akin to those of the Gaussian orthogonal ensemble.
10 pages, six references. Fuller version with correct proof of important theorem