TY - CHAP
T1 - On the Geometry of Random Polytopes
AU - Mendelson, Shahar
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - We present a simple proof to a fact recently established in Guédon et al. (Commun Contemp Math (to appear, 2018). arXiv:1811.12007): let ξ be a symmetric random variable that has variance 1, let Γ = (ξij) be an N × n random matrix whose entries are independent copies of ξ, and set X1, …, XN to be the rows of Γ. Then under minimal assumptions on ξ and as long as N ≥ c1n, with high probability c2(B∞n∩log(eN∕n)B2n)⊂absconv(X1,…,XN).(Formula
AB - We present a simple proof to a fact recently established in Guédon et al. (Commun Contemp Math (to appear, 2018). arXiv:1811.12007): let ξ be a symmetric random variable that has variance 1, let Γ = (ξij) be an N × n random matrix whose entries are independent copies of ξ, and set X1, …, XN to be the rows of Γ. Then under minimal assumptions on ξ and as long as N ≥ c1n, with high probability c2(B∞n∩log(eN∕n)B2n)⊂absconv(X1,…,XN).(Formula
UR - http://www.scopus.com/inward/record.url?scp=85088509410&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-46762-3_8
DO - 10.1007/978-3-030-46762-3_8
M3 - Chapter
T3 - Lecture Notes in Mathematics
SP - 187
EP - 198
BT - Lecture Notes in Mathematics
PB - Springer
ER -