A1279
Title: Large deviations for the volume of k-nearest neighbor balls
Authors: Takashi Owada - Purdue University (United States) [presenting]
Christian Hirsch - Aarhus University (Denmark)
Taegyu Kang - Purdue University (United States)
Abstract: The large deviations theory is developed for the point process associated with the Euclidean volume of k-nearest neighbour balls centred around the points of a homogeneous Poisson or a binomial point process in the unit cube. Two different types of large deviation behaviours of such point processes are investigated. The first result is the Donsker-Varadhan large deviation principle, under the assumption that the centring terms for the volume of k-nearest neighbour balls grow to infinity more slowly than those needed for Poisson convergence. Additionally, large deviations are also studied based on the notion of M0-topology, which takes place when the centring terms tend to infinitely sufficiently fast, compared to those for Poisson convergence. As applications of the main theorems, large deviations are discussed for the number of Poisson or binomial points of degree at most k in a random geometric graph in the dense regime.
