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Fast mixing of a randomized shift-register Markov chain
Published online by Cambridge University Press: 02 September 2022
Abstract
We present a Markov chain on the n-dimensional hypercube $\{0,1\}^n$ which satisfies $t_{{\rm mix}}^{(n)}(\varepsilon) = n[1 + o(1)]$ . This Markov chain alternates between random and deterministic moves, and we prove that the chain has a cutoff 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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- © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust