  In this note, we design a discrete random walk on the real line which takes
steps $0, \pm 1$ (and one with steps in $\{\pm 1, 2\}$) where at least $96\%$
of the signs are $\pm 1$ in expectation, and which has $\mathcal{N}(0,1)$ as a
stationary distribution. As an immediate corollary, we obtain an online version
of Banaszczyk's discrepancy result for partial colorings and $\pm 1, 2$
signings. Additionally, we recover linear time algorithms for logarithmic
bounds for the Koml\'{o}s conjecture in an oblivious online setting.
