2020/06/12 by Newman, Andrew
#52A22 #52B05 #60C05 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)
paper · doi:10.48550/arxiv.2006.07000
A two-step model for generating random polytopes is considered. For parameters d, m, and p, the first step is to generate a simple polytope P whose facets are given by m uniform random hyperplanes tangent to the unit sphere in ℝd, and the second step is to sample each vertex of P independently with probability p and let Q be the convex hull of the sampled vertices. We establish results on how well Q approximates the unit sphere in terms of m and p as well as asymptotics on the combinatorial complexity of Q for certain regimes of p.