论文标题
在空间随机网络中的强度加权边缘长度的上部大偏差
Upper large deviations for power-weighted edge lengths in spatial random networks
论文作者
论文摘要
我们研究了基于Poisson的空间随机网络中功率加权边缘长度$ \ sum_ {e \ e} | e |^α$的大批量渐近学。在制度$α> d $中，我们提供了一组足够的条件，在这些条件下，上部大偏差渐近造成的特征是凝结现象，这意味着多余的部分是由泊松点的一部分引起的。此外，速率函数可以通过具体优化问题表示。该框架特别包含了$ K $ neart nearbor图的指示，折叠和无向变体，以及合适的$β$ - 骨骼。
We study the large-volume asymptotics of the sum of power-weighted edge lengths $\sum_{e \in E}|e|^α$ in Poisson-based spatial random networks. In the regime $α> d$, we provide a set of sufficient conditions under which the upper large deviations asymptotics are characterized by a condensation phenomenon, meaning that the excess is caused by a negligible portion of Poisson points. Moreover, the rate function can be expressed through a concrete optimization problem. This framework encompasses in particular directed, bidirected and undirected variants of the $k$-nearest neighbor graph, as well as suitable $β$-skeletons.
