{
  "abstract": "We study geometry-controlled, initial-density-dependent stationary states in exclusion processes with branching-merging structures. We consider two boundary geometries for connecting the parallel branches to the reservoirs: the \\(1\\)-\\(n\\)-\\(1\\) model, in which a single lane branches into \\(n\\) parallel lanes and then merges back into a single lane, and the \\(0\\)-\\(n\\)-\\(0\\) model, in which particles directly enter and leave the \\(n\\) parallel lanes. For both models, we derive critical initial densities separating the low-density, shock-wave, and high-density regimes, and show that the theoretical predictions reproduce the phase diagrams and branch-averaged densities observed in simulations. In the \\(1\\)-\\(n\\)-\\(1\\) geometry, the critical initial densities depend on both the number of branches and the lengths of the upstream and downstream single-lane segments, whereas in the \\(0\\)-\\(n\\)-\\(0\\) geometry the corresponding estimates depend only on the number of branches. These results show that initial-condition dependence can arise from the global geometry of a branching-merging exclusion process, even without an explicit friction rule at the merging point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15333",
  "author_total": 3,
  "authors": [
    {
      "name": "Hiroki Yamamoto"
    },
    {
      "name": "Daichi Yanagisawa"
    },
    {
      "name": "Katsuhiro Nishinari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8zzc5ycaphr1c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15333",
  "fulltext_url": null,
  "id": "8zzc5ycaphr1c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15333",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "nlin.CG"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7221784858",
  "pdf_url": "https://arxiv.org/pdf/2610.15333",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8zzc5ycaphr1c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.15333",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15333"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.CG",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Geometry-Controlled Initial-Density Dependence in Branching-Merging Exclusion Processes",
  "title_text": "Geometry-Controlled Initial-Density Dependence in Branching-Merging Exclusion Processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/8zzc5ycaphr1c",
  "venue": "arXiv",
  "versions": []
}