随机在线最近邻图的极限理论
Limit theory for the random on-line nearest-neighbour graph
摘要：
在联机最近邻图（ONG）中，在R^d中的点序列中的第一个点之后的每个点通过边连接到序列中在它之前的那些点中的最近邻点。本文研究了（0，1）^d中一致随机点上ONG总幂加权长度的大样本渐近性态。特别地，当d=1且重量指数α>1/2时，中心总重量的极限分布可用分布不动点方程来表征。作为辅助结果，我们给出了单位区间内均匀随机点上标准最近邻（有向）图的期望和方差的精确表达式。
英文摘要：
In the on-line nearest-neighbour graph (ONG), each point after the first in a sequence of points in R^d is joined by an edge to its nearest-neighbour amongst those points that precede it in the sequence. We study the large-sample asymptotic behaviour of the total power-weighted length of the ONG on uniform random points in (0,1)^d. In particular, for d=1 and weight exponent α>1/2, the limiting distribution of the centred total weight is characterized by a distributional fixed-point equation. As an ancillary result, we give exact expressions for the expectation and variance of the standard nearest-neighbour (directed) graph on uniform random points in the unit interval.
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