dorsal/arxiv
View SchemaLocal Density of Activated Random Walk on $\mathbb{Z}$
| Authors | Christopher Hoffman, Jacob Richey, Hyojeong Son |
|---|---|
| Categories | |
| ArXiv ID | 2601.07816vv1 |
| URL | https://arxiv.org/abs/2601.07816 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We consider one-dimensional activated random walk (ARW) on $\mathbb{Z}$ started from a `point source' initial condition, with many particles at the origin and no other particles. We prove that, uniformly throughout a macroscopic window around the source, the probability that a site contains a sleeping particle after the configuration is stabilized is approximately the critical density. This represents a first step towards understanding the local structure of the critical stationary measure for ARW.
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"abstract": "We consider one-dimensional activated random walk (ARW) on $\\mathbb{Z}$ started from a `point source\u0027 initial condition, with many particles at the origin and no other particles. We prove that, uniformly throughout a macroscopic window around the source, the probability that a site contains a sleeping particle after the configuration is stabilized is approximately the critical density. This represents a first step towards understanding the local structure of the critical stationary measure for ARW.",
"arxiv_id": "2601.07816",
"authors": [
"Christopher Hoffman",
"Jacob Richey",
"Hyojeong Son"
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"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Local Density of Activated Random Walk on $\\mathbb{Z}$",
"url": "https://arxiv.org/abs/2601.07816",
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