{
  "abstract": "Consider the one-dimensional elliptic operator given by (Lϵf)(x)=b(x)f′(x)+ϵa(x)f″(x), where the drift b:R→R and the diffusion coefficient a:R→R are periodic C1(R) functions satisfying further conditions, and ϵ>0. Consider the initial-valued problem ∂tuϵ=Lϵuϵ,uϵ(0,⋅)=u0(⋅), for some bounded continuous function u0. We prove the existence of time-scales θϵ(1),…,θϵ(q) such that θϵ(1)→∞, θϵ(p+1)∕θϵ(p)→∞, 1≤p≤q−1, probability measures p(x,⋅), x∈R, and kernels Rt(p)(mj,mk), where {mj:j∈Z} represents the set of stable equilibrium of the ODE x˙(t)=b(x(t)) such that limϵ→0uϵ(tθϵ(p),x)=∑j,k∈Zp(x,mj)Rt(p)(m j,mk)u0(mk), for all t>0 and x∈R. The solution uϵ asymptotic behaviour description is completed by the characterisation of its behaviour in the intermediate time-scales ϱϵ such that ϱϵ∕θϵ(p)→∞, ϱϵ∕θϵ(p+1)→0 for some 0≤p≤q, where θϵ(0)=1, θϵ(q+1)=+∞. The proof relies on the analysis of the diffusion Xϵ(⋅) induced by the generator Lϵ based on the resolvent approach to metastability introduced in [21].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2505.20217",
  "author_total": 2,
  "authors": [
    {
      "name": "Claudio Landim"
    },
    {
      "name": "Christian Maura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5cdm40mfjgm0r.bib",
  "cited_by": 0,
  "doi": "10.1214/26-ejp1606",
  "fulltext_url": null,
  "id": "5cdm40mfjgm0r",
  "issns": [
    "1083-6489"
  ],
  "landing_url": "https://hal.science/hal-05770845v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "1703|Advanced Mathematical Modeling in Engineering"
    ]
  ],
  "openalex": "W4414588303",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": "Institute of Mathematical Statistics (IMS)",
  "ris": "https://research.draconitic.com/paper/5cdm40mfjgm0r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:44Z",
      "native_id": "hal-05770845",
      "source": "hal",
      "url": "https://hal.science/hal-05770845v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:1083-6489",
      "subfield": "probability"
    }
  ],
  "title": "From one-dimensional diffusion processes metastable behaviour to parabolic equations asymptotics",
  "title_text": "From one-dimensional diffusion processes metastable behaviour to parabolic equations asymptotics",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:44Z",
  "url": "https://research.draconitic.com/paper/5cdm40mfjgm0r",
  "venue": "Electronic Journal of Probability",
  "versions": []
}