Variance asymptotics and scaling limits for Gaussian polytopes

DOI10.1007/s00440-014-0592-6zbMath1360.60030arXiv1403.1010OpenAlexW2004843172MaRDI QIDQ748444

Pierre Calka, Joseph E. Yukich

Publication date: 29 October 2015

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

Full work available at URL: https://arxiv.org/abs/1403.1010

zbMATH Keywords

Burgers' equationconvex hullrandom polytopePoisson point processparabolic germ-grain models

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Asymptotic theory of convex bodies (52A23)

Related Items (17)

Gaussian polytopes: a cumulant-based approach ⋮ The -Delaunay tessellation: Description of the model and geometry of typical cells ⋮ The \(\beta \)-Delaunay tessellation. II: the Gaussian limit tessellation ⋮ Variance asymptotics and scaling limits for random polytopes ⋮ Convex hulls of random walks: expected number of faces and face probabilities ⋮ Limit theory for the first layers of the random convex hull peeling in the unit ball ⋮ Limit theorems for the volumes of small codimensional random sections of \(\ell_{p}^{n}\)-balls ⋮ Sectional Voronoi tessellations: characterization and high-dimensional limits ⋮ The β-Delaunay tessellation IV: Mixing properties and central limit theorems ⋮ Facets of high-dimensional Gaussian polytopes ⋮ Convex hulls of perturbed random point sets ⋮ Intrinsic volumes and Gaussian polytopes: the missing piece of the jigsaw ⋮ Normal approximation for statistics of Gibbsian input in geometric probability ⋮ Brownian cuboid and its geometric characteristics ⋮ Limit theorems for random polytopes with vertices on convex surfaces ⋮ Expected volumes of Gaussian polytopes, external angles, and multiple order statistics ⋮ Gaussian convex bodies: a nonasymptotic approach

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