{
  "abstract": "We study interview positioning in the secretary problem when an applicant is uncertain about their own absolute rank. The employer uses a given rejection threshold, and the applicant's self-rank distribution is truncated geometric. We show that the applicant need only compare the first eligible position with the final position and that, for finite $n$, a unique critical value exists precisely when $r(r+1)>n-1$. If $r_n$ is the employer's rejection threshold and $r_n/n\\toα\\in(0,1)$ as $n\\to\\infty$, then \\[ \\lim_{n\\to\\infty}q_c(n,r_n) = q_c(α) = \\frac{1-α}{1-α+α^2}. \\] Thus uncertainty about absolute rank produces an explicit asymptotic phase transition in optimal interview positioning.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11826",
  "author_total": 1,
  "authors": [
    {
      "name": "Jose Á. Islas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brwcnebgaz0rj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11826",
  "fulltext_url": null,
  "id": "brwcnebgaz0rj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11826",
  "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.PR"
    ],
    [
      "openalex",
      "1705|Optimization and Search Problems"
    ]
  ],
  "openalex": "W7212299371",
  "pdf_url": "https://arxiv.org/pdf/2609.11826",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brwcnebgaz0rj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2609.11826",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11826"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Strategic Interview Positioning under Uncertain Self-Rank",
  "title_text": "Strategic Interview Positioning under Uncertain Self-Rank",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/brwcnebgaz0rj",
  "venue": "arXiv",
  "versions": []
}