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 Banaszczyks 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.
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