{
  "abstract": "We consider fluctuations of the spin current in the stochastic XNOR process, a kinetically constrained hopping model in one spatial dimension. We formulate three conjectures with explicit amplitudes for the long-time current distributions: a Gaussian limit on the $t^{1/4}$ scale for homogeneous initial states with nonzero magnetization, a half-normal limit on the $t^{1/4}$ scale for domain-wall states with opposite magnetizations, and an M-Wright limit on the $t^{1/8}$ scale for homogeneous initial states at zero magnetization. Earlier work identified the tracer mechanism and anticipated the scaling exponents and limiting shapes in the domain-wall and zero-magnetization settings. Starting from the microscopic XNOR dynamics, we predict the missing amplitudes for the continuous-time process and extend the picture to homogeneous biased initial data. Simulations provide numerical support for all three conjectures without fitted parameters. A separate mathematical companion paper presents an extensively AI-generated candidate proof. Generative-AI tools were used in the research and writing workflow.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.10536",
  "author_total": 1,
  "authors": [
    {
      "name": "Balázs Pozsgay"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8sp5edtznr0wh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.10536",
  "fulltext_url": null,
  "id": "8sp5edtznr0wh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.10536",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7202255360",
  "pdf_url": "https://arxiv.org/pdf/2608.10536",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8sp5edtznr0wh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2608.10536",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.10536"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Anomalous current fluctuations in the stochastic XNOR hopping model",
  "title_text": "Anomalous current fluctuations in the stochastic XNOR hopping model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/8sp5edtznr0wh",
  "venue": "arXiv",
  "versions": []
}