Random cones in high dimensions II: Weyl cones

We consider two models of random cones together with their duals. Let Y 1 , ⋯ n $Y_1,\dots ,Y_n$ be independent and identically distributed vectors in R d $\mathbb {R}^d$ whose distribution satisfies some mild condition. The G A $G_{n,d}^A$ B $G_{n,d}^B$ are defined as the positive hulls pos { − 2 } $\mbox{pos}\lbrace Y_1-Y_2,\dots ,Y_{n-1}-Y_n\rbrace$ respectively, ,Y_{n-1}-Y_n,Y_n\rbrace$ conditioned on event that respective hull is not equal to . prove limit theorems for various expected geometric functionals these cones, tend infinity a coordinated way. This includes number k-faces kth conic quermassintegrals, n, sometimes also k simultaneously. Moreover, we uncover phase transition high dimensions statistical dimension both cones.