{
  "abstract": "Modern effective field theories of dissipative hydrodynamics, built on the Schwinger-Keldysh (SK) formalism, include thermal noise that is not Gaussian. The resultant higher-order noise vertices are constrained by symmetries, but otherwise treated as free parameters. We show explicitly that symmetry constraints alone do not guarantee these vertices yield a genuine probability distribution. Requiring a probability interpretation yields sharp bounds between cumulants that are invisible to the symmetry analysis. The bounds are optimal: their boundaries are attained by explicit positive distributions, and constructive completions are provided for both negative- and positive-kurtosis noise data. This gives closed-form nonlinear response and an exact sampling algorithm, whose Monte Carlo implementation reproduces the exact cumulants and nonlinear fluctuation-dissipation relations. Confronted with microscopic results, the framework places a sharp lower bound on the time step required for a positive stochastic completion of a quartic model of the Brownian particle used in the literature, while holographically computed $SU(2)$ noise vertices pass a nontrivial continuum fourth-order positivity test.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12050",
  "author_total": 2,
  "authors": [
    {
      "name": "Andrea Amoretti"
    },
    {
      "name": "Daniel K. Brattan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/05f30tyqes2jq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12050",
  "fulltext_url": null,
  "id": "05f30tyqes2jq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12050",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|High-Energy Particle Collisions Research"
    ]
  ],
  "openalex": "W7212807360",
  "pdf_url": "https://arxiv.org/pdf/2609.12050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/05f30tyqes2jq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.12050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12050"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Staying positive: bounds for non-Gaussian noise in Schwinger-Keldysh effective field theory",
  "title_text": "Staying positive: bounds for non-Gaussian noise in Schwinger-Keldysh effective field theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:52Z",
  "url": "https://research.draconitic.com/paper/05f30tyqes2jq",
  "venue": "arXiv",
  "versions": []
}