{
  "abstract": "For a $d$-dimensional probability vector $\\mathbf{h}=(h_1,\\dots, h_d)$, let $(S^{\\mathbf{h}}_n)_{n\\geq 0}$ be a nearest-neighbor random walk on $\\mathbb{Z}^d$ such that at each step, it moves to one of the two nearest neighbors in the $i$-th dimension with probability $\\frac{1}{2} h_i$ ($i=1,\\dots, d$). Let $T^{\\mathbf{h}}=\\inf\\{n\\geq 1: S^{\\mathbf{h}}_n=(0,\\dots,0)\\}$, the first return time to the origin. For two $d$-dimensional probability vectors $\\mathbf{h}'$ and $\\mathbf{h}''$ with the former majorizing the latter, we show that $T^{\\mathbf{h}'}$ is stochastically smaller than $T^{\\mathbf{h}''}$. In particular, the first return time for the $d$-dimensional simple random walk is stochastically larger than $T^{\\mathbf{h}}$ for all $d$-dimensional probability vectors $\\mathbf{h}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36728",
  "author_total": 3,
  "authors": [
    {
      "name": "Shoou-Ren Hsiau"
    },
    {
      "name": "Ting-Yi Tsai"
    },
    {
      "name": "Yi-Ching Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3nztm5ny3h566.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36728",
  "fulltext_url": null,
  "id": "3nztm5ny3h566",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36728",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7214907554",
  "pdf_url": "https://arxiv.org/pdf/2609.36728",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3nztm5ny3h566.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36728",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36728"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stochastic dominance of first return times for nearest-neighbor random walks on $\\mathbb{Z}^d$",
  "title_text": "Stochastic dominance of first return times for nearest-neighbor random walks on ℤ^d",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/3nztm5ny3h566",
  "venue": "arXiv",
  "versions": []
}