{
  "abstract": "Random multiplicative growth with redistribution generates stationary Pareto wealth tails in the Bouchaud-Mézard model, but assumes a fixed multiplicative noise intensity. This is restrictive for physical and financial growth processes, where volatility (diffusivity) is often fluctuating. We replace the constant noise intensity by a switching diffusivity and ask how these fluctuations select the Pareto stationary tail. For a geometric Brownian motion with switching diffusivity, the long-time Gaussian limit holds when the redraw law has finite mean and variance. The asymptotic variance retains a contribution from diffusivity persistence. With redistribution and a general redraw law, the stationary large-wealth problem is characterized by a spectral condition for admissible algebraic modes. For a two-state diffusivity, an exact tail analysis gives a Pareto exponent interpolating between the high-diffusivity slow-refresh limit and the mean-diffusivity fast-refresh Bouchaud-Mézard limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.19464",
  "author_total": 2,
  "authors": [
    {
      "name": "Maxence Arutkin"
    },
    {
      "name": "Alexandre Vallée"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cp2y9avpcgqtf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.19464",
  "fulltext_url": null,
  "id": "cp2y9avpcgqtf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.19464",
  "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"
    ],
    [
      "openalex",
      "2002|Complex Systems and Time Series Analysis"
    ]
  ],
  "openalex": "W7161797687",
  "pdf_url": "https://arxiv.org/pdf/2605.19464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cp2y9avpcgqtf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2605.19464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.19464"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Switching diffusivity selects Pareto tail exponent in random growth with redistribution",
  "title_text": "Switching diffusivity selects Pareto tail exponent in random growth with redistribution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:03Z",
  "url": "https://research.draconitic.com/paper/cp2y9avpcgqtf",
  "venue": "arXiv",
  "versions": []
}