{
  "abstract": "We study a model of heterogeneous multiplicative growth with mean-field redistribution and independent local stochastic resetting. The model describes populations or wealth distributed over sites with quenched growth-rate heterogeneity, while resets represent random local extinction or bankruptcy events. At large redistribution or resetting rate, we find a delocalized phase and we compute the growth rate as well as the stationary distribution of the population of a given site. We show that reset-free growth episodes generate power-law stationary tails with site-dependent exponents. For weak resetting and redistribution, favorable sites can undergo long reset-free episodes and localize. This produces a partially localized phase, in which a finite fraction of the total population is carried by a small set of sites whose identity changes on an $O(1)$ time scale within a subextensive pool of $N^{u^\\star}$ favorable candidates, with $0<u^\\star<1$. We derive the corresponding growth rate from a saddle point analysis, and show that the averaged stationary fractions display multifractal behavior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22038",
  "author_total": 4,
  "authors": [
    {
      "name": "Maximilien Bernard"
    },
    {
      "name": "Giuseppe Del Vecchio Del Vecchio"
    },
    {
      "name": "Jean-Philippe Bouchaud"
    },
    {
      "name": "Pierre Le Doussal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1c4130e0fnag8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22038",
  "fulltext_url": null,
  "id": "1c4130e0fnag8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22038",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "econ.TH"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7222411473",
  "pdf_url": "https://arxiv.org/pdf/2610.22038",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1c4130e0fnag8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.22038",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22038"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Partial Localization and Multifractality in Heterogeneous Population Growth with Resetting",
  "title_text": "Partial Localization and Multifractality in Heterogeneous Population Growth with Resetting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:55Z",
  "url": "https://research.draconitic.com/paper/1c4130e0fnag8",
  "venue": "arXiv",
  "versions": []
}