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arXiv · 2109.05387

Fast mixing of a randomized shift-register Markov chain

David A. Levin·Chandan Tankala
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Abstract

We present a Markov chain on the $n$-dimensional hypercube $\{0,1\}^n$ which satisfies $t_{{\rm mix}}(\epsilon) = n[1 + o(1)]$. This Markov chain alternates between random and deterministic moves and we prove that the chain has cut-off with a window of size at most $O(n^{0.5+\delta})$ where $\delta>0$. The deterministic moves correspond to a linear shift register.

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David A. Levin, Chandan Tankala. 2021-09-11. Fast mixing of a randomized shift-register Markov chain. https://arxiv.org/abs/2109.05387

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