{
  "abstract": "Non-Gaussian stationary fluctuations with heavy tails and finite-order moment cutoffs are ubiquitous in non-equilibrium systems. Here, we derive the Pearson type IV distribution as the stationary solution of a standardized Fokker-Planck equation with linear drift and quadratic diffusion. We establish necessary and sufficient conditions for its emergence and show that the linear-quadratic structure, although sufficient, is not necessary. We also give explicit closed expressions for the cumulative distribution function, a moment recurrence relation, skewness, kurtosis, and mode. From a physical perspective, our results reveal that heavy tails and asymmetry originate from distinct features of state-dependent diffusion: its local nonlinear curvature and gradient, respectively. In particular, asymmetric stationary fluctuations can emerge even in the presence of a symmetric linear restoring drift. This framework provides a general stochastic description of asymmetric heavy-tailed fluctuations in non-equilibrium systems, including space plasma turbulence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06749",
  "author_total": 4,
  "authors": [
    {
      "name": "Daniele Belardinelli"
    },
    {
      "name": "Simone Benella"
    },
    {
      "name": "Mirko Stumpo"
    },
    {
      "name": "Giuseppe Consolini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ncd8w11e3rxn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06749",
  "fulltext_url": null,
  "id": "0ncd8w11e3rxn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06749",
  "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",
      "physics.flu-dyn"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06749",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ncd8w11e3rxn.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.06749",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06749"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "A Drift-Diffusion Approach for Pearson Type IV Heavy-Tail Distributions",
  "title_text": "A Drift-Diffusion Approach for Pearson Type IV Heavy-Tail Distributions",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:21Z",
  "url": "https://research.draconitic.com/paper/0ncd8w11e3rxn",
  "venue": "arXiv",
  "versions": []
}