{
  "abstract": "Let $(c_t)_{t\\geq 0}$ be a deterministic family of edge conductances on a countable vertex set, monotone in $t$, and let $(X_t)$ be the random walk that takes its $t$-th step using the conductances $c_t$. We prove that if $c_t\\uparrow c_\\infty$ and $c_\\infty$ is recurrent (respectively, $c_0$ is transient), then $(X_t)$ is almost surely recurrent (respectively, transient), i.e., visits every vertex infinitely (respectively, finitely) often. We also establish the analogous results in continuous time. This proves conjectures of Amir, Benjamini, Gurel-Gurevich, and Kozma, and the special case of $\\{ 0, 1 \\}$-valued conductances corresponds to simple random walk on a growing graph, and in this special case our results prove a conjecture of Dembo, Huang, and Sidoravicius. In addition, we provide counterexamples to the corresponding conjectures when $(c_t)$ is monotone non-increasing: if $c_t\\downarrow c_\\infty$ and $c_\\infty$ is transient, $(X_t)$ need not be transient, and similarly if $c_0$ is recurrent, $(X_t)$ need not be recurrent, even if $c_\\infty\\geqαc_0$ for some $α>0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28848",
  "author_total": 2,
  "authors": [
    {
      "name": "Rupert Li"
    },
    {
      "name": "Jiyun Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7nnzm0jacty44.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28848",
  "fulltext_url": null,
  "id": "7nnzm0jacty44",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28848",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7214322104",
  "pdf_url": "https://arxiv.org/pdf/2609.28848",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7nnzm0jacty44.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.28848",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28848"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Recurrence and transience of random walks in monotonically changing environments",
  "title_text": "Recurrence and transience of random walks in monotonically changing environments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/7nnzm0jacty44",
  "venue": "arXiv",
  "versions": []
}