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arXiv · 2510.05514

The odometer in subcritical activated random walk

Tobias Johnson·Jacob Richey
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Abstract

We consider the activated random walk particle system, a model of self-organized criticality, on $\mathbb{Z}$ with i.i.d.-Bernoulli initial configuration. We show that at subcritical density, the system's odometer function, which counts the number of actions taken at each site, has a stretched exponential tail. It follows that the expected odometer at each site is finite.

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Tobias Johnson, Jacob Richey. 2025-10-07. The odometer in subcritical activated random walk. https://arxiv.org/abs/2510.05514

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