{
  "abstract": "For a one-dimensional path graph and a lifted path graph constructed from a duplication of each of its sites, we study how a reversible Markov chain can be perturbed and gradually driven into non-reversibility. The reversible Markov chain has a transition matrix that is diagonalizable and features real-valued eigenvalues and eigenvectors. The left and right eigenvectors form a biorthogonal system. We discuss in concrete examples how the transition matrix of a non-reversible Markov chain may be diagonalizable or non-diagonalizable, and it may have real eigenvalues and complex-conjugate pairs. For a number of steady states (flat, square-wave, wedge, V-shape), we compute eigenvalue spectra on both graphs and discuss the speedup that can be achieved through lifting. We develop a Green's matrix formalism, which we use to compute Kemeny times and mean first-passage times, and which provides valuable information and allows us to interpret the results for the characteristic times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05183",
  "author_total": 3,
  "authors": [
    {
      "name": "Gustave Robichon"
    },
    {
      "name": "Cecile Monthus"
    },
    {
      "name": "Werner Krauth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27g6xzt4cz2j1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05183",
  "fulltext_url": null,
  "id": "27g6xzt4cz2j1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05183",
  "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",
      "cond-mat.stat-mech"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.05183",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27g6xzt4cz2j1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:14Z",
      "native_id": "2609.05183",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05183"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Markov chains at the onset of non-reversibility",
  "title_text": "Markov chains at the onset of non-reversibility",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:14Z",
  "url": "https://research.draconitic.com/paper/27g6xzt4cz2j1",
  "venue": "arXiv",
  "versions": []
}