Probability Distribution of Curvatures of Isosurfaces in Gaussian Random Fields

摘要

An expression for the joint probability distribution of the principalcurvatures at an arbitrary point in the ensemble of isosurfaces defined onisotropic Gaussian random fields on Rn is derived. The result is obtained byderiving symmetry properties of the ensemble of second derivative matrices ofisotropic Gaussian random fields akin to those of the Gaussian orthogonalensemble.