Gaussian fluctuations for edge counts in high-dimensional random geometric graphs

DOI10.1016/j.spl.2019.108674zbMath1453.60015arXiv1612.03286OpenAlexW2990895133MaRDI QIDQ2288829

Christoph Thäle, Jens Grygierek

Publication date: 20 January 2020

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.03286

zbMATH Keywords

stochastic geometrycentral limit theoremPoisson point processsecond-order Poincaré inequalityedge counting statistichigh dimensional random geometric graph

Mathematics Subject Classification ID

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

Related Items (4)

Random geometric graph: some recent developments and perspectives ⋮ Limit theory of sparse random geometric graphs in high dimensions ⋮ Phase transitions for detecting latent geometry in random graphs ⋮ Poisson and Gaussian fluctuations for the $\mathbf{f}$-vector of high-dimensional random simplicial complexes

Cites Work

• Stochastic analysis for Poisson point processes. Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry
• High-dimensional random geometric graphs and their clique number
• Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization
• Limit theory for the Gilbert graph
• Central limit theorems for \(U\)-statistics of Poisson point processes
• Testing for high-dimensional geometry in random graphs
• Random Geometric Graphs

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