Multivariate normal approximation in geometric probability

DOI10.1080/15598608.2008.10411876zbMath1420.60010arXiv0707.3898OpenAlexW3101895756MaRDI QIDQ2324084

Andrew R. Wade, Mathew D. Penrose

Publication date: 13 September 2019

Published in: Journal of Statistical Theory and Practice (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.3898

zbMATH Keywords

stabilizationStein's methodcentral limit theoremgeometric probabilitymultivariate normal approximationnearest-neighbour graph

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Random measures (60G57)

Related Items

Limit Theorems in Discrete Stochastic Geometry, Rates of multivariate normal approximation for statistics in geometric probability, Geometric probability on the sphere, Continuum percolation for Cox point processes, Poisson process Fock space representation, chaos expansion and covariance inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• On normal approximations of distributions in terms of dependency graphs
• On the rate of convergence in the multivariate CLT
• Gaussian limits for generalized spacings
• On central limit theorems in geometrical probability
• Gaussian limits for random measures in geometric probability
• The central limit theorem for weighted minimal spanning trees on random points
• Weak laws of large numbers in geometric probability
• Limit theory for random sequential packing and deposition
• Central limit theorems for some graphs in computational geometry.
• Normal approximation under local dependence.
• A multivariate CLT for local dependence with \(n^{-1/2}\log n\) rate and applications to multivariate graph related statistics
• Gaussian limits for random geometric measures
• Laws of large numbers in stochastic geometry with statistical applications
• Multivariate spatial central limit theorems with applications to percolation and spatial graphs
• Explicit laws of large numbers for random nearest-neighbour-type graphs
• Random Geometric Graphs
• Multivariate normal approximations by Stein's method and size bias couplings
• Limit theory for the random on‐line nearest‐neighbor graph
• Probability