TY - GEN A1 - Kaibel, Volker A1 - Remshagen, Anja T1 - On the Graph-Density of Random 0/1-Polytopes N2 - Abstract. Let Xd,n be an n-element subset of {0, 1}d chosen uniformly at random, and denote by Pd,n := conv Xd,n its convex hull. Let ∆d,n be the density of the graph of Pd,n (i.e., the number of one-dimensional faces of Pd,n divided by n ). Our main result is that, for any function 2 n(d), the expected value of ∆d,n(d) converges (with d → ∞) to one if, √ for some arbitrary ε < 0, n(d) ≤ ( 2 − ε)d holds for all large d, while it √ converges to zero if n(d) ≥ ( 2 + ε)d holds for all large d. Y1 - 2003 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/13 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-136 ER -