Polynomial parallel volume, convexity and contact distributions of random sets

DOI10.1007/s00440-005-0459-yzbMath1099.60011OpenAlexW2085204686MaRDI QIDQ2492621

Daniel Hug, Günter Last, Wolfgang Weil

Publication date: 14 June 2006

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-005-0459-y

zbMATH Keywords

Boolean modelLinear sectionPlanar section

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Length, area, volume, other geometric measure theory (28A75) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Integral geometry (53C65) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (8)

Anisotropic tubular neighborhoods of sets ⋮ Stationary Apollonian packings ⋮ Mean Densities and Spherical Contact Distribution Function of Inhomogeneous Boolean Models ⋮ A general formula for the anisotropic outer Minkowski content of a set ⋮ The parallel volume at large distances ⋮ Local empirical processes near boundaries of convex bodies ⋮ The derivative of the parallel volume difference ⋮ Curvature measures and soap bubbles beyond convexity

Cites Work

• Maximal volume enclosed by plates and proof of the chessboard conjecture
• Does polynomial parallel volume imply convexity?
• On support measures in Minkowski spaces and contact distributions in stochastic geometry.
• Weakly Differentiable Functions
• A Quasi-Poisson Point-Process in the Plane
• First contact distributions for spatial patterns: regularity and estimation
• Continuum Percolation
• Random processes of Hausdorff rectifiable closet sets
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