Gaussian processes, kinematic formulae and Poincaré's limit

DOI10.1214/08-AOP439zbMath1172.60006arXivmath/0612580OpenAlexW3101903889MaRDI QIDQ838005

Robert J. Adler, Jonathan E. Taylor

Publication date: 21 August 2009

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

Full work available at URL: https://arxiv.org/abs/math/0612580

zbMATH Keywords

geometryEuler characteristicGaussian fieldsexcursion setsintrinsic volumeskinematic formulaePoincaré's limit

Mathematics Subject Classification ID

Random fields (60G60) Random fields; image analysis (62M40) Gaussian processes (60G15) Extreme value theory; extremal stochastic processes (60G70) Sample path properties (60G17) Differentiable manifolds, foundations (58A05) Differential geometric aspects in kinematics (53A17)

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Cites Work

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• A dozen de Finetti-style results in search of a theory
• Euler characteristics for Gaussian fields on manifolds
• On excursion sets, tube formulas and maxima of random fields.
• Integral geometry of tame sets
• Testing for a signal with unknown location and scale in a stationary Gaussian random field
• Estimating the number of peaks in a random field using the Hadwiger characteristic of excursion sets, with applications to medical images
• A Gaussian kinematic formula
• Validity of the expected Euler characteristic heuristic
• Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ ², F and t Fields
• Testing for signals with unknown location and scale in a χ²random field, with an application to fMRI
• Lipschitz–Killing Invariants
• Boundary corrections for the expected Euler characteristic of excursion sets of random fields, with an application to astrophysics
• Random Fields and Geometry
• The Distribution of the Maxima of a Random Curve
• On the Volume of Tubes
• Mathematical Analysis of Random Noise
• Analytic and geometric study of stratified spaces