2018/04/16 by Schneider, Rolf
#60D05 #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)
paper · doi:10.48550/arxiv.1804.05622
For a stationary Poisson hyperplane tessellation X in \mathbb Rd, whose directional distribution satisfies some mild conditions (which hold in the isotropic case, for example), it was recently shown that with probability one every combinatorial type of a simple d-polytope is realized infinitely often by the polytopes of X. This result is strengthened here: with probability one, every such combinatorial type appears among the polytopes of X not only infinitely often, but with positive density.