The size of components in continuum nearest-neighbor graphs
成果类型：
Article
署名作者：
Kozakova, Iva; Meester, Ronald; Nanda, Seema
署名单位：
Vrije Universiteit Amsterdam; Tata Institute of Fundamental Research (TIFR); University of Tennessee System; University of Tennessee Knoxville
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117905000000729
发表日期：
2006
页码：
528-538
关键词：
摘要：
We study the size of connected components of random nearest-neighbor graphs with vertex set the points of a homogeneous Poisson point process in R-d. 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.