Zakhar Kabluchko, University of Münster, Germany, Expected f-vector of the Poisson Zero Cell
ZoomThe Poisson hyperplane process describes, roughly speaking, infinitely many hyperplanes thrown uniformly at random into the d-dimensional Euclidean space. The hyperplanes dissect the space into countably many cells. The a.s. unique cell containing the origin is called the Poisson zero polytope. We prove an explicit combinatorial formula for the expected number of k-dimensional faces of…