## The Annals of Probability

### The size of components in continuum nearest-neighbor graphs

#### Abstract

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

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

Dates
First available in Project Euclid: 9 May 2006

https://projecteuclid.org/euclid.aop/1147179981

Digital Object Identifier
doi:10.1214/009117905000000729

Mathematical Reviews number (MathSciNet)
MR2223950

Zentralblatt MATH identifier
1111.60076

#### Citation

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. https://projecteuclid.org/euclid.aop/1147179981

#### References

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