A large-dimensional independent and identically distributed property for nearest neighbor counts in Poisson processes

DOI10.1214/aoap/1034968144zbMath0870.60045OpenAlexW2056022166MaRDI QIDQ1814751

Yi-Ching Yao, Gordon Simons

Publication date: 1 September 1997

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1034968144

zbMATH Keywords

Poisson point processBernoulli random variablesnearest neighbor counts

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (4)

On the number of weakly connected subdigraphs in random \(k\)NN digraphs ⋮ Rate of Poisson approximation for nearest neighbor counts in large-dimensional Poisson point processes ⋮ On variances of partial volumes of the typical cell of a Poisson-Voronoi tessellation and large-dimensional volume degeneracy ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Nearest neighbor analysis of point processes: Applications to multidimensional scaling
• On the reciprocity of proximity relations
• Nearest neighbors and Voronoi regions in certain point processes
• Nearest neighbors and Voronoi volumes in high-dimensional point processes with various distance functions
• On the probability that a random point is the jth nearest neighbour to its own kth nearest neighbour
• Mutual and shared neighbor probabilities: finite- and infinite-dimensional results
• On the fraction of random points by specified nearest-neighbour interrelations and degree of attraction
• Reflexive Nearest Neighbours
• Isolated nearest neighbors
• Nearest neighbours in a Poisson ensemble

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