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Stationary activated random walk: regularity, heavy tails, and remixing
Abstract
We study the stationary state of driven-dissipative activated random walk on an interval of length n and prove that subintervals down to size log n have particle density near the critical value. We then deduce that the avalanche area is heavy-tailed and that the process forgets an initial stationary state after o(n) steps. We conjecture that the density fluctuations, avalanche area, and remixing time from stationarity are governed by the same critical exponent.
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BibTeX
@misc{johnson2026stationary,
title = {{Stationary activated random walk: regularity, heavy tails, and remixing}},
author = {Tobias Johnson and Matthew Junge and Josh Meisel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31843},
eprint = {2609.31843},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31843},
}
RIS
TY - UNPB
TI - Stationary activated random walk: regularity, heavy tails, and remixing
AU - Tobias Johnson
AU - Matthew Junge
AU - Josh Meisel
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31843
UR - https://arxiv.org/abs/2609.31843
AB - We study the stationary state of driven-dissipative activated random walk on an interval of length n and prove that subintervals down to size log n have particle density near the critical value. We then deduce that the avalanche area is heavy-tailed and that the process forgets an initial stationary state after o(n) steps. We conjecture that the density fluctuations, avalanche area, and remixing time from stationarity are governed by the same critical exponent.
ER -