{
  "abstract": "We study the moments of | det (H -E)| q and the large deviations of the corresponding reduced intensive log spectral determinant e for random matrix operators with Laplacian and random-potential terms. For large N and real q > -1, we obtain a closed saddle-point characterization of the exponential growth rates Σ q in arbitrary dimension. This yields the large-deviation form P (e) ∼ exp {-NL d Φ(e)} and an explicit expression for the rate function Φ(e). The framework includes Hessians of random elastic manifolds at generic energy configurations. In one dimension, these become N × N matrix-valued random Schrödinger operators, and log| det(H -E)| is the sum of the N Lyapunov exponents. A stochastic matrix Riccati mapping relates their spectral properties to the total N-particle current of Dyson Brownian motion (DBM) in a cubic potential. Allez and Dumaz [J. Stat. Phys. 160(3), 681-714 (2015)] showed that at N = ∞ this model has a sharp transition between a current-carrying and a confined phase. We compute the DBM barrier-crossing probability at large finite N, yielding the exponential tail of the mean density of states below the spectral edge. The barrier scales as ∼ N(-E) 3/2 at large negative energy and vanishes as ∼ N(E * -E) 5/4 near the edge. For q = 1 we also obtain an independent derivation of the total complexity of stationary points for a disordered elastic string embedded in N dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2511.00954",
  "author_total": 3,
  "authors": [
    {
      "name": "Yan V Fyodorov"
    },
    {
      "name": "Pierre Le Doussal"
    },
    {
      "name": "Alexander Ossipov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7psd8g100hx2v.bib",
  "cited_by": 0,
  "doi": "10.1063/5.0351290",
  "fulltext_url": null,
  "id": "7psd8g100hx2v",
  "issns": [
    "0022-2488"
  ],
  "landing_url": "https://hal.science/hal-05825130v1",
  "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|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W4416434693",
  "pdf_url": "https://hal.science/hal-05825130/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": "American Institute of Physics (AIP)",
  "ris": "https://research.draconitic.com/paper/7psd8g100hx2v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:59Z",
      "native_id": "hal-05825130",
      "source": "hal",
      "url": "https://hal.science/hal-05825130v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Spectral Theory in Mathematical Physics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Large deviations of spectral determinants of matrix-valued random Schrödinger operators and Dyson Brownian motion in cubic potentials",
  "title_text": "Large deviations of spectral determinants of matrix-valued random Schrödinger operators and Dyson Brownian motion in cubic potentials",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:59Z",
  "url": "https://research.draconitic.com/paper/7psd8g100hx2v",
  "venue": "Journal of Mathematical Physics",
  "versions": []
}