Expected Number and Height Distribution of Critical Points of Smooth Isotropic Gaussian Random Fields

• Published in: Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability Vol. 24; no. 4B; p. 3422
• Main Authors: Cheng, Dan, Schwartzman, Armin
• Format: Journal Article
• Language: English
• Published: England 01.11.2018
• Subjects: GOI; Critical points; 60G60; Gaussian random fields; Boundary; 15B52; Sphere; Height density; Random matrices; Kac-Rice formula; Isotropic; GOE; 60G15

We obtain formulae for the expected number and height distribution of critical points of 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 t...