{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31843",
  "author_total": 3,
  "authors": [
    {
      "name": "Tobias Johnson"
    },
    {
      "name": "Matthew Junge"
    },
    {
      "name": "Josh Meisel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/02y2b4d3b820c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31843",
  "fulltext_url": null,
  "id": "02y2b4d3b820c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31843",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7214720488",
  "pdf_url": "https://arxiv.org/pdf/2609.31843",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/02y2b4d3b820c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31843",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31843"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stationary activated random walk: regularity, heavy tails, and remixing",
  "title_text": "Stationary activated random walk: regularity, heavy tails, and remixing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/02y2b4d3b820c",
  "venue": "arXiv",
  "versions": []
}