{
  "abstract": "We study random walks with geometric or log-gamma increments, reweighted by certain exponential functionals. We establish precise asymptotics for all moments of exponential functionals, revealing a phase transition as the drifts of the walks vary. To describe the large time limit of reweighted random walks, we introduce a discrete $T$ transformation on random walk paths and establish Girsanov relations. As a corollary, we show that the stationary measures of geometric last passage percolation and the log-gamma polymer on a strip converge to their half-space counterparts as the strip width tends to infinity. In the log-gamma case, this provides an alternative proof of a recent result in arXiv:2607.17030.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19673",
  "author_total": 1,
  "authors": [
    {
      "name": "Zikun Ouyang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9nd34thzw3p6d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19673",
  "fulltext_url": null,
  "id": "9nd34thzw3p6d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19673",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  ],
  "openalex": "W7222149053",
  "pdf_url": "https://arxiv.org/pdf/2610.19673",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9nd34thzw3p6d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.19673",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19673"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Exponential functionals of two random walks and stationary measures of discrete growth processes",
  "title_text": "Exponential functionals of two random walks and stationary measures of discrete growth processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/9nd34thzw3p6d",
  "venue": "arXiv",
  "versions": []
}