{
  "abstract": "We establish linear time precutoff for oriented kinetically constrained models (KCMs) on a $d$-dimensional box of side length $n$, whenever the finite-volume spectral gap is bounded away from zero uniformly in $n$. A typical example is the North-East model, a $0$-$1$ spin system on the two-dimensional integer lattice that evolves according to the following rule: whenever a site's southerly and westerly nearest neighbours have spin $0$, with rate one it resets its own spin by tossing a $(1-q)$-coin; at all other times its spin remains frozen. This settles, in the oriented case, a conjecture which states that there is linear time precutoff for all KCMs in the (open) ergodic parameter regime ($q>q_c$). The result has been shown recently, for general update families, in a perturbative regime ($q$ close to $1$). The previous general upper bound on the mixing time for oriented update families, in the full ergodic regime, was $O(n \\log n)$. The proof combines a spectral estimate for a certain killed process with a graphical coupling to a stationary process and a backward witness path argument, exploiting the orientation of the constraints, to control the probability of failing to couple.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30585",
  "author_total": 1,
  "authors": [
    {
      "name": "Paul Chleboun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ewkkh2qbzf1d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30585",
  "fulltext_url": null,
  "id": "2ewkkh2qbzf1d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30585",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7214666132",
  "pdf_url": "https://arxiv.org/pdf/2609.30585",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ewkkh2qbzf1d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30585",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30585"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Linear time mixing and pre-cutoff for oriented kinetically constrained models",
  "title_text": "Linear time mixing and pre-cutoff for oriented kinetically constrained models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/2ewkkh2qbzf1d",
  "venue": "arXiv",
  "versions": []
}