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arXiv · 2501.17938

Cutoff for activated random walk

Christopher Hoffman·Tobias Johnson·Matthew Junge·Josh Meisel
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Abstract

We prove that the mixing time of driven-dissipative activated random walk on an interval of length $n$ with uniform or central driving exhibits cutoff at $n$ times the critical density for activated random walk on the integers. The proof uses a new result for arbitrary graphs showing that the chain is mixed once activity is likely at every site.

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Christopher Hoffman, Tobias Johnson, Matthew Junge, Josh Meisel. 2025-01-29. Cutoff for activated random walk. https://arxiv.org/abs/2501.17938

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