Probability Distribution of Curvatures of Isosurfaces in Gaussian Random Fields

An expression for the joint probability distribution of the principal curvatures at an arbitrary point in the ensemble of isosurfaces defined on isotropic Gaussian rando m fields on R n 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 ensemb le.