{
  "abstract": "We study the persistence probabilities of a moving average process of order one with innovations that follow a Laplace distribution. The persistence probabilities can be computed fully explicitly in terms of classical combinatorial quantities like certain $q$-Pochhammer symbols or $q$-deformed analogues of Euler's zigzag numbers, respectively. Similarly, the generating functions of the persistence probabilities can be written in terms of $q$-analogues of the exponential function or the $q$-sine/$q$-cosine functions, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Frank Aurzada"
    },
    {
      "name": "Kilian Raschel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fnsqpbsg65hqy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2512.14152",
  "fulltext_url": null,
  "id": "fnsqpbsg65hqy",
  "issns": [],
  "landing_url": "https://hal.science/hal-05844982v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-co"
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    [
      "hal",
      "1.math.math-pr"
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    [
      "openalex",
      "2613|Probability and Statistical Research"
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  "openalex": "W4417466896",
  "pdf_url": "https://hal.science/hal-05844982/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fnsqpbsg65hqy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:03Z",
      "native_id": "hal-05844982",
      "source": "hal",
      "url": "https://hal.science/hal-05844982v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-co",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-pr",
      "subfield": "probability"
    }
  ],
  "title": "Persistence probabilities of MA(1) sequences with Laplace innovations and q-deformed zigzag numbers",
  "title_text": "Persistence probabilities of MA(1) sequences with Laplace innovations and q-deformed zigzag numbers",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:45Z",
  "url": "https://research.draconitic.com/paper/fnsqpbsg65hqy",
  "venue": "HAL",
  "versions": []
}