Singularities of Gaussian Random Maps into the Plane

2022/02/16 by Mishal Assif P K, K, Mishal Assif P
Computer Science · Earth and Planetary Sciences · Environmental Science · Mathematics · #FOS: Mathematics #Geology and Paleoclimatology Research #Geometric Topology (math.GT) #Image Processing and 3D Reconstruction #Landslides and related hazards #Probability (math.PR) #math.GT #math.PR

paper · pdf · doi:10.48550/arxiv.2202.08242

arxiv created 2022/02/16 · openalex publication_date 2022/02/16 · arxiv updated 2022/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the expected value of various quantities related to the biparametric singularities of a pair of smooth centered Gaussian random fields on an n-dimensional compact manifold, such as the lengths of the critical curves and contours of a fixed index and the number of cusps. We obtain certain expressions under no particular assumptions other than smoothness of the two fields, but more explicit formulae are derived under varying levels of additional constraints such as the two random fields being i.i.d, stationary, isotropic etc.

Related

• Expected Number and Height Distribution of Critical Points of Smooth Isotropic Gaussian Random Fields
• On critical points of Gaussian random fields under diffeomorphic transformations
• Expected number density of critical points of smooth Gaussian random fields in arbitrary dimensions
• Smooth Matérn Gaussian Random Fields: Euler Characteristic, Expected Number and Height Distribution of Critical Points
• Excursion Probabilities of Isotropic and Locally Isotropic Gaussian Random Fields on Manifolds