Stochastic and Integral Geometry

By Rolf Schneider, Wolfgang H. Weil. 2008

484 citations recorded by the source corpus.

Subfields: Computer Graphics and Computer-Aided Design, Geometry and Topology, Signal Processing

View Paper: https://www.semanticscholar.org/paper/3ce4a6d66ec4eed360826e6d88d63a4fcd4e3a48

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Citations in the corpus

$\mathrm{GL}(n)$ contravariant Minkowski valuations (2012, unknown): “, [8, 18, 27, 28, 35, 36, 39, 40].”
Estimation of geodesic tortuosity and constrictivity in stationary random closed sets (2018, background): “For the standard Voronoi tessellation in R3 with generating points in normal position, it is a classical result that any four cells meet in at most one point (Schneider and Weil, 2008).”
Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry (2014, methodology): “d of Bd(0,r) for short. For r≥0, the Minkowski sum Kr =K+rBd of Kand rBd is the so-called r-parallel set of K. In particular, if Kis a convex set with nonempty interior, Steiner’s formula (see, e.g., [38], equation (14.5)) says that the volume vol(Kr) is a polynomial of degree din r. Formally, vol(K”
Random geometric complexes in the thermodynamic regime (2014, methodology): “We refer readers to the standard texts such as [16, 25] for more details on the topology we need, while [34, 38] covers the point process material.”
New Berry-Esseen bounds for non-linear functionals of Poisson random measures (2013, background): “It is random closed set in the sense of [35] if ∫ Kd 0 vol(K + C)M(dK) <∞ for all compact sets C ⊂ R, where + stands for the usual Minkowski addition and vol( · ) for the Lebesgue measure on R.”
Expected intrinsic volumes and facet numbers of random beta‐polytopes (2017, methodology): “unit sphere, respectively, in a linear subspace L ∈ G(d,k), and by k·kE, Bk E, S k−1 E , λE and σE the respective objects in an aﬃne subspace E ∈ A(d,k). This is the same notation as used in the book [35], to which we refer for further information. Furthermore, we use the symbol ∆k(x0,...,xk) = Volk”
Minkowski valuations and generalized valuations (2015, background): “where SO(n) = SO(n) nR (see the books [39, 58] for more information).”
Beta polytopes and Poisson polyhedra: f-vectors and angles (2018, background): “Both models are classical objects in stochastic geometry and well studied; we refer to [25, 35] for further background material.”
Lectures on the Poisson Process (2017, methodology): “We shall also introduce the intrinsic volumes of convex bodies, referring to [147] and [146] for further detail.”