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March 2006 The size of components in continuum nearest-neighbor graphs
Iva Kozakova, Ronald Meester, Seema Nanda
Ann. Probab. 34(2): 528-538 (March 2006). DOI: 10.1214/009117905000000729


We study the size of connected components of random nearest-neighbor graphs with vertex set the points of a homogeneous Poisson point process in ℝd. The connectivity function is shown to decay superexponentially, and we identify the exact exponent. From this we also obtain the decay rate of the maximal number of points of a path through the origin. We define the generation number of a point in a component and establish its asymptotic distribution as the dimension d tends to infinity.


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Iva Kozakova. Ronald Meester. Seema Nanda. "The size of components in continuum nearest-neighbor graphs." Ann. Probab. 34 (2) 528 - 538, March 2006.


Published: March 2006
First available in Project Euclid: 9 May 2006

zbMATH: 1111.60076
MathSciNet: MR2223950
Digital Object Identifier: 10.1214/009117905000000729

Primary: 60D05 , 60G55 , 60K35

Keywords: continuum percolation , nearest-neighbor connections , Poisson process , Random graphs , size of components

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 2 • March 2006
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