The Annals of Probability

The size of components in continuum nearest-neighbor graphs

Iva Kozakova, Ronald Meester, and Seema Nanda

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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.

Article information

Ann. Probab., Volume 34, Number 2 (2006), 528-538.

First available in Project Euclid: 9 May 2006

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G55: Point processes 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Continuum percolation Poisson process size of components nearest-neighbor connections random graphs


Kozakova, Iva; Meester, Ronald; Nanda, Seema. The size of components in continuum nearest-neighbor graphs. Ann. Probab. 34 (2006), no. 2, 528--538. doi:10.1214/009117905000000729.

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