Central limit theorems for the radial spanning tree1. Issue 2 (9th April 2016)

• Record Type: Journal Article
• Authors: Schulte, Matthias; Thäle, Christoph
• Is Part Of: Random structures & algorithms. Volume 50:Issue 2(2017)
• Page Start: 262
• Page End: 286
• Publication Date: 2016-04-09
• Subjects: central limit theorem -- directed spanning forest -- Poisson point process -- radial spanning tree -- random graph; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20651
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: 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