{
  "abstract": "Stochastic inflation is a powerful technique for calculating the probability distribution function (PDF) of large inflationary perturbations, which may collapse to form Primordial Black Holes. The PDF, $P({\\cal N})$, of the stochastic number of e-folds, ${\\cal N}$, satisfies an adjoint Fokker-Planck Equation. We develop a new self-contained eigenvalue technique which can be used to determine $P({\\cal N})$. First we apply this method to the simple case of quantum diffusion along a flat potential without any classical drift. We recover the expression for the PDF that has previously been found using characteristic functions, with an exponential tail, and a power-law behaviour, $P({\\cal N}) \\propto {\\cal N}^{-3/2}$, in the intermediate regime between the peak and the tail of the PDF. Finally we apply the method to constant drift inflation, in the narrow- and broad-well limits. In the narrow-well limit, there is an analytic solution and the PDF is similar to the drift-free case, with a mildly suppressed tail. In the broad-well limit, determining the full set of eigenvalues and eigenfunctions requires a piecewise construction of the spectrum, and the broad-well PDF is qualitatively different, with an enhanced peak and a strongly suppressed tail.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.00176",
  "author_total": 3,
  "authors": [
    {
      "name": "Swagat S. Mishra"
    },
    {
      "name": "Edmund J. Copeland"
    },
    {
      "name": "Anne M. Green"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3jgf6bp9nm3nq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.00176",
  "fulltext_url": null,
  "id": "3jgf6bp9nm3nq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.00176",
  "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",
      "astro-ph.CO"
    ],
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.00176",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3jgf6bp9nm3nq.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:24Z",
      "native_id": "2606.00176",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.00176"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Eigenvalue formulation of Stochastic Inflation and application to large perturbation generating inflationary features",
  "title_text": "Eigenvalue formulation of Stochastic Inflation and application to large perturbation generating inflationary features",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/3jgf6bp9nm3nq",
  "venue": "arXiv",
  "versions": []
}