A Slight Improvement to the Colored Bárány's Theorem [article]

Zilin Jiang
2014 arXiv   pre-print
Suppose d+1 absolutely continuous probability measures m_0, ..., m_d on R^d are given. In this paper, we prove that there exists a point of R^d that belongs to the convex hull of d+1 points v_0, ..., v_d with probability at least 2d/(d+1)!(d+1), where each point v_i is sampled independently according to probability measure m_i.
arXiv:1405.2503v2 fatcat:4deh2fsutjgjvfwafvaxh4dsqy