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Central limit theorems for the radial spanning tree
Author(s) -
Schulte Matthias,
Thäle Christoph
Publication year - 2017
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20651
Subject(s) - mathematics , point process , poisson point process , limit (mathematics) , euclidean space , poisson distribution , regular polygon , combinatorics , spanning tree , random tree , euclidean geometry , tree (set theory) , point (geometry) , cox process , mathematical analysis , poisson process , geometry , computer science , statistics , motion planning , artificial intelligence , robot
Consider a homogeneous Poisson point process in a compact convex set in d ‐dimensional Euclidean space which has interior points and contains the origin. The radial spanning tree is constructed by connecting each point of the Poisson point process with its nearest neighbour that is closer to the origin. For increasing intensity of the underlying Poisson point process the paper provides expectation and variance asymptotics as well as central limit theorems with rates of convergence for a class of edge functionals including the total edge length. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 262–286, 2017