Expected Number and Height Distribution of Critical Points of Smooth Isotropic Gaussian Random Fields
نویسندگان
چکیده
Abstract: We obtain formulae for the expected number and height distribution of critical points of general smooth isotropic Gaussian random fields parameterized on Euclidean space or spheres of arbitrary dimension. The results hold in general in the sense that there are no restrictions on the covariance function of the field except for smoothness and isotropy. The results are based on a characterization of the distribution of the Hessian of the Gaussian field by means of the family of Gaussian orthogonally invariant (GOI) matrices, of which the Gaussian orthogonal ensemble (GOE) is a special case. Explicit formulae are shown for 2 and 3-dimensional fields.
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