A Gaussian fixed point random walk

Yang P. Liu; Ashwin Sah; Mehtaab Sawhney

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arXiv · 2104.07009

A Gaussian fixed point random walk

Yang P. Liu·Ashwin Sah·Mehtaab Sawhney

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Abstract

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.

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Yang P. Liu, Ashwin Sah, Mehtaab Sawhney. 2021-04-14. A Gaussian fixed point random walk. https://arxiv.org/abs/2104.07009

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