  We study discrepancy minimization for vectors in $\mathbb{R}^n$ under various
settings. The main result is the analysis of a new simple random process in
multiple dimensions through a comparison argument. As corollaries, we obtain
bounds which are tight up to logarithmic factors for several problems in online
vector balancing posed by Bansal, Jiang, Singla, and Sinha (STOC 2020), as well
as linear time algorithms for logarithmic bounds for the Koml\'{o}s conjecture.
