U-Statistics in Stochastic Geometry

DOI10.1007/978-3-319-05233-5_7zbMath1528.60046arXiv1503.00110OpenAlexW1841132204MaRDI QIDQ6067401

Raphael Lachieze-Rey, Matthias Reitzner

Publication date: 17 November 2023

Published in: Stochastic Analysis for Poisson Point Processes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.00110

zbMATH Keywords

stochastic geometryPoisson processPoisson point processintrinsic volumeconcentration inequality

Mathematics Subject Classification ID

Statistics on manifolds (62R30) Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Large deviations (60F10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (8)

Limit theory for U-statistics under geometric and topological constraints with rare events ⋮ Concentration for Poisson \(U\)-statistics: subgraph counts in random geometric graphs ⋮ The fourth moment theorem on the Poisson space ⋮ The Malliavin–Stein Method on the Poisson Space ⋮ Poisson Point Process Convergence and Extreme Values in Stochastic Geometry ⋮ U-Statistics on the Spherical Poisson Space ⋮ Introduction to Stochastic Geometry ⋮ Large deviation principle for geometric and topological functionals and associated point processes

Cites Work

• Normal approximation of Poisson functionals in Kolmogorov distance
• Limit theorems for Betti numbers of random simplicial complexes
• Fine Gaussian fluctuations on the Poisson space. I: Contractions, cumulants and geometric random graphs
• Random geometric complexes
• Multi-dimensional Gaussian fluctuations on the Poisson space
• The scaling limit of Poisson-driven order statistics with applications in geometric probability
• Poisson point processes: large deviation inequalities for the convex distance
• Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering
• Dimension free and infinite variance tail estimates on Poisson space
• A central limit theorem for generalized multilinear forms
• Stein's method and normal approximation of Poisson functionals
• Central limit theorems for Poisson hyperplane tessellations
• Symmetric statistics, Poisson point processes, and multiple Wiener integrals
• Covariances of symmetric statistics
• Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities
• Sylvester's question: The probability that \(n\) points are in convex position
• On logarithmic Sobolev inequalities for continuous time random walks on graphs
• A central limit theorem for the Poisson-Voronoi approximation
• Concentration and deviation inequalities in infinite dimensions via covariance representations
• Limit theory for the Gilbert graph
• Central limit theorems for \(U\)-statistics of Poisson point processes
• Fine Gaussian fluctuations on the Poisson space. II: Rescaled kernels, marked processes and geometric \(U\)-statistics
• New Berry-Esseen bounds for non-linear functionals of Poisson random measures
• Intersection and proximity of processes of flats
• A four moments theorem for Gamma limits on a Poisson chaos
• Gamma limits and U-statistics on the Poisson space
• Topology of random simplicial complexes: a survey
• Random Geometric Graphs
• Simplicial Homology of Random Configurations
• Moments and Central Limit Theorems for Some Multivariate Poisson Functionals
• The Malliavin–Stein Method on the Poisson Space
• Stochastic Analysis for Poisson Processes
• Introduction to Stochastic Geometry

This page was built for publication: U-Statistics in Stochastic Geometry