TY - JOUR
T1 - Threshold phenomena for high-dimensional random polytopes
AU - Bonnet, Gilles
AU - Chasapis, Giorgos
AU - Grote, Julian
AU - Temesvari, Daniel
AU - Turchi, Nicola
PY - 2019
Y1 - 2019
N2 - Let ํ1,โฆ,ํํ, ํ>ํ, be independent random points in โํ, distributed according to the so-called beta or beta-prime distribution, respectively. We establish threshold phenomena for the volume, intrinsic volumes, or more general measures of the convex hulls of these random point sets, as the space dimension ํ tends to infinity. The dual setting of polytopes generated by random halfspaces is also investigated.
AB - Let ํ1,โฆ,ํํ, ํ>ํ, be independent random points in โํ, distributed according to the so-called beta or beta-prime distribution, respectively. We establish threshold phenomena for the volume, intrinsic volumes, or more general measures of the convex hulls of these random point sets, as the space dimension ํ tends to infinity. The dual setting of polytopes generated by random halfspaces is also investigated.
UR - https://arxiv.org/pdf/1802.04089.pdf
U2 - 10.1142/S0219199718500384
DO - 10.1142/S0219199718500384
M3 - Article
SN - 1793-6683
VL - 21
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
IS - 5
M1 - 1850038
ER -