{
  "abstract": "We establish conditional limit theorems, pointwise in the initial state, for absorbing Markov chains on a compact metric space $M$. We assume $L^1(M,ρ)$-continuous transition densities, irreducibility and aperiodicity. For the observable $f_β(x)=d_M(x,x_0)^{-β}$, with suitable $x_0$ satisfying $ρ(B_r(x_0))\\sim C_d(x_0)r^d$, we prove that the point-process of normalised observations converges to a Poisson random measure. This yields totally right-skewed $α$-stable laws for $α=d/β\\in(0,2)$ and, at the boundary value $α=2$, a Gaussian limit with the non-standard normalisation $\\sqrt{n\\log n}$. We also establish a conditional central limit theorem for $L^2$ observables, exponential deviation bounds for bounded observables and a conditional Poisson law for visits to shrinking targets. The results and remarks have been formalised in Lean~4.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22499",
  "author_total": 2,
  "authors": [
    {
      "name": "Bernat Bassols Cornudella"
    },
    {
      "name": "Matheus M Castro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c7wtxfr6x71a8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22499",
  "fulltext_url": null,
  "id": "c7wtxfr6x71a8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22499",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214036222",
  "pdf_url": "https://arxiv.org/pdf/2609.22499",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c7wtxfr6x71a8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2609.22499",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22499"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Conditional Stable Laws and Rare-Event Limits for Absorbing Markov Chains",
  "title_text": "Conditional Stable Laws and Rare-Event Limits for Absorbing Markov Chains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/c7wtxfr6x71a8",
  "venue": "arXiv",
  "versions": []
}