Topological complexity of smooth random functions. École d'Été de Probabilités de Saint-Flour XXXIX-2009.

DOI10.1007/978-3-642-19580-8zbMath1230.60001OpenAlexW571062441MaRDI QIDQ630636

Jonathan E. Taylor, Robert J. Adler

Publication date: 18 March 2011

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-19580-8

zbMATH Keywords

Riemannian manifoldsGaussian random fieldstopological inferenceGaussian kinematic formulaLipschitz-Killing curvature

Mathematics Subject Classification ID

Gaussian processes (60G15) Geometric probability and stochastic geometry (60D05) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory (60-01)

Related Items (18)

Topology of random geometric complexes: a survey ⋮ A quantitative central limit theorem for the Euler-Poincaré characteristic of random spherical eigenfunctions ⋮ The mean Euler characteristic and excursion probability of Gaussian random fields with stationary increments ⋮ Point pattern analysis of spatial deformation and blurring effects on exceedances ⋮ Pattern Size in Gaussian Fields from Spinodal Decomposition ⋮ Statistical proof? The problem of irreproducibility ⋮ On the excursion area of perturbed Gaussian fields ⋮ Asymptotic expansion of the expected Minkowski functional for isotropic central limit random fields ⋮ Approximate normality of high-energy hyperspherical eigenfunctions ⋮ Hadwiger's theorem for definable functions ⋮ Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization ⋮ Statistical Topology and the Random Interstellar Medium ⋮ A reduction principle for the critical values of random spherical harmonics ⋮ Fluctuations of the Euler-Poincaré characteristic for random spherical harmonics ⋮ The volume-of-tube method for Gaussian random fields with inhomogeneous variance ⋮ Tropical Sufficient Statistics for Persistent Homology ⋮ Lipschitz-Killing Curvatures of the Excursion Sets of Skew Student'stRandom Fields ⋮ High-frequency asymptotics for Lipschitz-Killing curvatures of excursion sets on the sphere

This page was built for publication: Topological complexity of smooth random functions. École d'Été de Probabilités de Saint-Flour XXXIX-2009.