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Random walks with $k$-wise independent increments

Itai Benjamini·Gady Kozma·Dan Romik
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Abstract

We construct examples of a random walk with pairwise-independent steps which is almost-surely bounded, and for any $m$ and $k$ a random walk with $k$-wise independent steps which has no stationary distribution modulo $m$.

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Itai Benjamini, Gady Kozma, Dan Romik. 2004-05-31. Random walks with $k$-wise independent increments. https://arxiv.org/abs/math/0405601

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