Cones generated by random points on half-spheres and convex hulls of Poisson point processes

@article{Kabluchko2018ConesGB,
  title={Cones generated by random points on half-spheres and convex hulls of Poisson point processes},
  author={Zakhar Kabluchko and Alexander Marynych and Daniel Temesvari and Christoph Th{\"a}le},
  journal={Probability Theory and Related Fields},
  year={2018},
  pages={1-41}
}
  • Zakhar Kabluchko, Alexander Marynych, +1 author Christoph Thäle
  • Published 2018
  • Mathematics
  • Probability Theory and Related Fields
  • Let $$U_1,U_2,\ldots $$U1,U2,… be random points sampled uniformly and independently from the d-dimensional upper half-sphere. We show that, as $$n\rightarrow \infty $$n→∞, the f-vector of the $$(d+1)$$(d+1)-dimensional convex cone $$C_n$$Cn generated by $$U_1,\ldots ,U_n$$U1,…,Un weakly converges to a certain limiting random vector, without any normalization. We also show convergence of all moments of the f-vector of $$C_n$$Cn and identify the limiting constants for the expectations. We prove… CONTINUE READING

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