Euler characteristics for Gaussian fields on manifolds

DOI10.1214/aop/1048516527zbMath1026.60039OpenAlexW1981225903MaRDI QIDQ1394517

Jonathan E. Taylor, Robert J. Adler

Publication date: 2 December 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1048516527

zbMATH Keywords

excursionsmanifoldsRiemannian geometryGaussian processesEuler characteristicrandom fields

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Differentiable manifolds, foundations (58A05) Differential geometric aspects in kinematics (53A17)

Related Items

Moderate deviation for random elliptic PDE with small noise, The mean Euler characteristic and excursion probability of Gaussian random fields with stationary increments, Gaussian processes, kinematic formulae and Poincaré's limit, Excursion probabilities of isotropic and locally isotropic Gaussian random fields on manifolds, Unnamed Item, Complexity of random smooth functions on the high-dimensional sphere, Testing One Hypothesis Multiple Times: The Multidimensional Case, Scalar curvature and \(Q\)-curvature of random metrics, The tube method for the moment index in projection pursuit, Critical probability of percolation over bounded region in N-dimensional Euclidean space, Average Euler characteristic of random real algebraic varieties, Euler characteristic heuristic for approximating the distribution of the largest eigenvalue of an orthogonally invariant random matrix, Tilted Euler characteristic densities for central limit random fields, with application to ``bubbles, Random fields of multivariate test statistics, with applications to shape analysis, Kinematic formula for heterogeneous Gaussian related fields, Detecting activation in fMRI data, Bicovariograms and Euler characteristic of random fields excursions, A Gaussian kinematic formula, On the distribution of the maximum of a Gaussian field with \(d\) parameters, Excursion probability of certain non-centered smooth Gaussian random fields, Rotation and scale space random fields and the Gaussian kinematic formula, The volume-of-tube method for Gaussian random fields with inhomogeneous variance, On the Density Functions of Integrals of Gaussian Random Fields, Lipschitz-Killing Curvatures of the Excursion Sets of Skew Student'stRandom Fields, Validity of the expected Euler characteristic heuristic, Unnamed Item, High-frequency asymptotics for Lipschitz-Killing curvatures of excursion sets on the sphere

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rotation space random fields with an application to fMRI data
• The detection of local shape changes via the geometry of Hotelling's \(T^2\) fields
• The geometry of correlation fields with an application to functional connectivity of the brain
• On excursion sets, tube formulas and maxima of random fields.
• On the equivalence of the tube and Euler characteristic methods for the distribution of the maximum of Gaussian fields over piecewise smooth domains
• Testing for a signal with unknown location and scale in a stationary Gaussian random field
• On the curvature of piecewise flat spaces
• Curvature Measures
• Morse Theory. (AM-51)
• Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ ², F and t Fields
• Boundary corrections for the expected Euler characteristic of excursion sets of random fields, with an application to astrophysics
• On the Volume of Tubes
• Riemannian geometry