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Introduction to Stochastic Geometry (Q6089028)

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scientific article; zbMATH DE number 7767014

Language	Label	Description	Also known as
English	Introduction to Stochastic Geometry	scientific article; zbMATH DE number 7767014

Statements

scholarly article

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Introduction to Stochastic Geometry (English)

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Matthias Reitzner

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Stochastic Analysis for Poisson Point Processes

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publication date

17 November 2023

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zbMATH Keywords

point process

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convex body

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Poisson point process

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Voronoi tessellation

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Boolean model

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MaRDI profile type

MaRDI publication profile

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Volume degeneracy of the typical cell and the chord length distribution for Poisson-Voronoi tessellations in high dimensions

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Random polytopes in smooth convex bodies

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Random polytopes in a convex polytope, independence of shape, and concentration of vertices

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Poisson polytopes

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On the variance of random polytopes

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Intrinsic volumes of inscribed random polytopes in smooth convex bodies

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Some distributional results for Poisson-Voronoi tessellations

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Gamma distributions for stationary Poisson flat processes

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Beyond the Efron-Buchta identities: distributional results for Poisson polytopes

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Asymptotic shape of small cells

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The critical probability for random Voronoi percolation in the plane is 1/2

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Stability of the reverse Blaschke-Santaló inequality for zonoids and applications

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Expectation of intrinsic volumes of random polytopes

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Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering

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The Malliavin–Stein Method on the Poisson Space

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Stochastische Approximation konvexer Polygone

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Limit theorems for functionals of convex hulls

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The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane

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Extreme values for characteristic radii of a Poisson-Voronoi tessellation

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Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius

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Large deviation probabilities for the number of vertices of random polytopes in the ball

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Variance asymptotics for random polytopes in smooth convex bodies

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Brownian limits, local limits and variance asymptotics for convex hulls in the ball

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A general study of extremes of stationary tessellations with examples

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Simplicial Homology of Random Configurations

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The monotonicity of \(f\)-vectors of random polytopes

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The convex hull of a random set of points

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The two-sample problem in $\Bbb R\sp m$ and measure-valued martingales

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On the mean value of the area of a random polygon in a plane convex body

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On a conjecture of D. G. Kendall concerning the planar Crofton cell and on its Brownian counterpart

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Foundations of quantization for probability distributions

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On some mean values associated with a randomly selected simplex in a convex set

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On the mean value of the volume of a random polytope in a convex set

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On the extension of additive functionals on classes of convex sets

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Limit theorems for convex hulls

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Stochastic Geometry for Wireless Networks

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Large deviations of the empirical volume fraction for stationary Poisson grain models

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Central limit theorem for a class of random measures associated with germ-grain models

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Limit theorems for stationary tessellations with random inner cell structures

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Poisson-Voronoi approximation

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On the Volume of the Zero Cell of a Class of Isotropic Poisson Hyperplane Tessellations

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Poisson polyhedra in high dimensions

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On the asymptotic distribution of the area outside a random convex hull in a disk

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Random Polytopes

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Asymptotic shapes of large cells in random tessellations

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Typical cells in Poisson hyperplane tessellations

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Large faces in Poisson hyperplane mosaics

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Faces with given directions in anisotropic Poisson hyperplane mosaics

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Approximation Properties of Random Polytopes Associated with Poisson Hyperplane Processes

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The limit shape of the zero cell in a stationary Poisson hyperplane tessellation.

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Large Poisson-Voronoi cells and Crofton cells

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Second-order properties and central limit theorems for geometric functionals of Boolean models

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Intersection and proximity of processes of flats

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Random geometric complexes

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Topology of random simplicial complexes: a survey

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Limit theorems for Betti numbers of random simplicial complexes

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On the almost sure coverage property of Voronoi tessellation: the ℝ<sup>1</sup> case

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Proof of David Kendall's conjecture concerning the shape of large random polygons

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A simplified proof of a conjecture of D. G. Kendall concerning shapes of random polygons

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Fine Gaussian fluctuations on the Poisson space. I: Contractions, cumulants and geometric random graphs

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Fine Gaussian fluctuations on the Poisson space. II: Rescaled kernels, marked processes and geometric \(U\)-statistics

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New Berry-Esseen bounds for functionals of binomial point processes

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U-Statistics in Stochastic Geometry

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Boundary density and Voronoi set estimation for irregular sets

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Stochastic Analysis for Poisson Processes

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Percolation on stationary tessellations: models, mean values, and second-order structure

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Poisson process Fock space representation, chaos expansion and covariance inequalities

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Moments and Central Limit Theorems for Some Multivariate Poisson Functionals

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Topological estimation of percolation thresholds

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Central limit theorems for random polygons in an arbitrary convex set

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Central limit theorems for uniform model random polygons

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Multi-dimensional Gaussian fluctuations on the Poisson space

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Stein's method and normal approximation of Poisson functionals

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Random Geometric Graphs

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Laws of large numbers in stochastic geometry with statistical applications

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ON THE MONOTONICITY OF THE EXPECTED VOLUME OF A RANDOM SIMPLEX

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Random polytopes and the Efron-Stein jackknife inequality.

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Central limit theorems for random polytopes

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The combinatorial structure of random polytopes

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Central limit theorems for \(U\)-statistics of Poisson point processes

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Set Reconstruction by Voronoi Cells

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Limit theory for the Gilbert graph

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�ber die konvexe H�lle von n zuf�llig gew�hlten Punkten

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�ber die konvexe H�lle von n zuf�llig gew�hlten Punkten. II

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Approximation of convex bodies by random polytopes

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A Duality for Poisson Flats

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Weighted faces of Poisson hyperplane tessellations

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Vertex numbers of weighted faces in Poisson hyperplane mosaics

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Extremal Properties of Random Mosaics

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Convex Bodies The Brunn-MinkowskiTheory

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Second moments related to Poisson hyperplane tessellations

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Stochastic and Integral Geometry

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Random polytopes in a convex body

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A central limit theorem for the Poisson-Voronoi approximation

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The scaling limit of Poisson-driven order statistics with applications in geometric probability

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Distances between Poisson \(k\)-flats

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Random Polytopes and Affine Surface Area

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Sharp concentration of random polytopes

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Surface order scaling in stochastic geometry

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Identifiers

zbMATH Open document ID

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10.1007/978-3-319-05233-5_5

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6089028

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