{
  "abstract": "In this paper, we study the spatial behavior of the solution ψ ( x , t ) to the stochastic heat equation ∂ t ψ ( x , t ) − 1 2 ∂ x 2 2 ψ ( x , t ) = g S ( x , t ) 2 ψ ( x , t ) , with 0 ⩽ t ⩽ T , x ∈ R , and ψ ( x , 0 ) = 1 . Here, g > 0 is a coupling constant and S ( x , t ) is a stationary, homogeneous, and ergodic Gaussian field. Focusing on E ( x , g ) ≡ ψ ( x , T ) at a finite time T > 0 , we identify the critical coupling g c ( T ) above which the average of E ( 0 , g ) diverges. We show that in the subcritical regime g < g c ( T ) , E ( x , g ) is spatially ergodic, with no intermittency, while in the supercritical regime g > g c ( T ) it becomes spatially intermittent and loses ergodicity. Our results differ from the extensively studied case where S ( x , t ) 2 is replaced by S ( x , t ) , in which intermittency appears only asymptotically as T → + ∞ , with no finite-time intermittency.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2601.18561",
  "author_total": 1,
  "authors": [
    {
      "name": "Philippe Mounaix"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8tvwpsknapm04.bib",
  "cited_by": 0,
  "doi": "10.1088/1751-8121/aea45e",
  "fulltext_url": null,
  "id": "8tvwpsknapm04",
  "issns": [
    "1751-8113",
    "1751-8121"
  ],
  "landing_url": "https://hal.science/hal-05755222v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.phys"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7125807323",
  "pdf_url": "https://hal.science/hal-05755222/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": "IOP Publishing",
  "ris": "https://research.draconitic.com/paper/8tvwpsknapm04.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:36Z",
      "native_id": "hal-05755222",
      "source": "hal",
      "url": "https://hal.science/hal-05755222v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Finite-time transition to intermittency for a stochastic heat equation driven by the square of a Gaussian field",
  "title_text": "Finite-time transition to intermittency for a stochastic heat equation driven by the square of a Gaussian field",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:36Z",
  "url": "https://research.draconitic.com/paper/8tvwpsknapm04",
  "venue": "Journal of Physics A: Mathematical and Theoretical",
  "versions": []
}