Limit theory for the random on‐line nearest‐neighbor graph

DOI10.1002/rsa.20185zbMath1147.60033arXivmath/0603561OpenAlexW2951738458MaRDI QIDQ5454356

Mathew D. Penrose, Andrew R. Wade

Publication date: 28 March 2008

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603561

zbMATH Keywords

weak convergencefixed-point equationdivide-and-conquernearest-neighbor graphspatial network evolution

Mathematics Subject Classification ID

Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) (L^p)-limit theorems (60F25)

Related Items (7)

A law of large numbers for nearest neighbour statistics ⋮ A Mecke-type formula and Markov properties for STIT tessellation processes ⋮ Limit theorems for random spatial drainage networks ⋮ Asymptotic theory for the multidimensional random on-line nearest-neighbour graph ⋮ Multivariate normal approximation in geometric probability ⋮ Quantitative two-scale stabilization on the Poisson space ⋮ Convergence in a Multidimensional Randomized Keynesian Beauty Contest

Cites Work

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• Probability theory of classical Euclidean optimization problems
• Asymptotic laws for nonconservative self-similar fragmentations
• Random Geometric Graphs

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