A0618
Title: Large deviation principle for geometric and topological functionals and associated point processes
Authors: Takashi Owada - Purdue University (United States) [presenting]
Abstract: A large deviation principle is proved for the point process associated with k-element connected components in the d-dimensional Euclidean space with respect to the connectivity radii as a function of sample size. The random points are generated from a homogeneous Poisson point process so that the connectivity radius is of the so-called sparse regime. The rate function for the obtained large deviation principle can be represented as relative entropy. As an application, we deduce large deviation principles for various functionals and point processes appearing in stochastic geometry and topology. As concrete examples of topological invariants, we consider persistent Betti numbers of geometric complexes and the number of Morse critical points of the min-type distance function.
