{
  "abstract": "We consider scaling limits of integer-valued random walks whose transition probabilities are translation-invariant everywhere except on a set that we will call a membrane or an interface. If the jumps outside the membrane are i.i.d. mean-zero random variables with finite variance, then possible examples of the corresponding limit processes include reflected Brownian motion, skew Brownian motion, and Brownian motion with a jump-type exit from zero. We also discuss the question of what the possible limits are if the jumps outside the membrane belong to the domain of attraction of a stable law.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17262",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrey Pilipenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ffyymr52sb57.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17262",
  "fulltext_url": null,
  "id": "6ffyymr52sb57",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17262",
  "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": "W7213402268",
  "pdf_url": "https://arxiv.org/pdf/2609.17262",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ffyymr52sb57.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17262",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17262"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Functional limit theorems for perturbed random walks",
  "title_text": "Functional limit theorems for perturbed random walks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/6ffyymr52sb57",
  "venue": "arXiv",
  "versions": []
}