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arXiv · 2408.07049

On the slow phase for fixed-energy Activated Random Walks

Bernardo N. B. de Lima·Leonardo T. Rolla·Célio Terra
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Abstract

We study the Activated Random Walk model on the one-dimensional ring, in the high density regime. We develop a toppling procedure that gradually builds an environment that can be used to show that activity will be sustained for a long time. This yields a self-contained and relatively short proof of existence of a slow phase for arbitrarily large sleep rates.

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Bernardo N. B. de Lima, Leonardo T. Rolla, Célio Terra. 2024-08-13. On the slow phase for fixed-energy Activated Random Walks. https://arxiv.org/abs/2408.07049

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