2017/04/08 by Zakhar Kabluchko, Kabluchko, Zakhar, Christoph Thäle +1
Computer Science · Mathematics · #51M20 (Secondary) #52A20 #52A22 #52B11 #60D05 (Primary) #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1704.02496
openalex publication_date 2017/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Pn be an n-dimensional regular polytope from one of the three\ninfinite series (regular simplices, regular crosspolytopes, and cubes). Project\nPn onto a random, uniformly distributed linear subspace of dimension d\≥\n2. We prove that the expected number of k-dimensional faces of the resulting\nrandom polytope is an increasing function of n. As a corollary, we show that\nthe expected number of k-faces of the Gaussian polytope is an increasing\nfunction of the number of points used to generate the polytope. Similar results\nare obtained for the symmetric Gaussian polytope and the Gaussian zonotope.\n