TY - UNPB
T1 - Upper large deviations for power-weighted edge lengths in spatial random networks
AU - Hirsch, Christian
AU - Willhalm, Daniel
PY - 2022/3/4
Y1 - 2022/3/4
N2 - We study the large-volume asymptotics of the sum of power-weighted edge lengths $\sum_{e\in E} |e|^\alpha$ in Poisson-based spatial random networks. In the regime $\alpha>d$, we provide a set of sufficient conditions under which the upper large deviations asymptotics are characterized by a condensation phenomena, 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 $\beta$-skeletons.
AB - We study the large-volume asymptotics of the sum of power-weighted edge lengths $\sum_{e\in E} |e|^\alpha$ in Poisson-based spatial random networks. In the regime $\alpha>d$, we provide a set of sufficient conditions under which the upper large deviations asymptotics are characterized by a condensation phenomena, 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 $\beta$-skeletons.
KW - large deviations
KW - condensation
KW - spatial random networks
KW - k-nearest neighbor graph
KW - beta-skeleton
U2 - 10.48550/arXiv.2203.02190
DO - 10.48550/arXiv.2203.02190
M3 - Preprint
BT - Upper large deviations for power-weighted edge lengths in spatial random networks
PB - arXiv
ER -