{
  "abstract": "We investigate the statistical properties and ergodic behavior of the absolute area below the trajectory of a particle subject to stochastic resetting and moving according to a scaled Brownian motion with exponent $β$. We compare the contributions to the absolute area from the waiting times between resets and the backward recurrence time. Using the renewal formalism we derive the lower-order moments of the absolute area under both Poissonian and heavy-tailed power-law resetting waiting time distributions with exponent $α$. For Poissonian resetting, stochastic interruption suppresses fluctuations, driving the area to be ergodic, regardless of the value of $β$. In contrast, power-law resetting yields a rich spectrum of ergodic regimes. For $0 < α< 1$, the system displays weak ergodicity breaking and the maximum contribution dominates the area accumulated during the waiting times. For $1+β< α< 2$, we unveil an ergodic transition exclusive to the subdiffusive regime at $α=1+β$, where ergodicity is restored. These results clarify the subtle interplay between anomalous diffusion and power-law waiting times between resettings. Our results are tested by numerical simulations exhibiting an excellent agreement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19985",
  "author_total": 2,
  "authors": [
    {
      "name": "Vicenç Méndez"
    },
    {
      "name": "Javier Cristín"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fd80bg99nt33s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19985",
  "fulltext_url": null,
  "id": "fd80bg99nt33s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19985",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7221906479",
  "pdf_url": "https://arxiv.org/pdf/2610.19985",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fd80bg99nt33s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.19985",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19985"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Absolute area under a scaled Brownian motion with resetting",
  "title_text": "Absolute area under a scaled Brownian motion with resetting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:31Z",
  "url": "https://research.draconitic.com/paper/fd80bg99nt33s",
  "venue": "arXiv",
  "versions": []
}